[Merged] Deeper than primes [Archive] - Page 49

epix

14th October 2010, 09:22 AM

The language that math speaks about a ≤ x ≤ b is based on collection of 0(), end exactly because a, x or b are no more than 0(), thay can't be 1(), which exists simultaneously at AND beyond the location of any given 0().

This fact is notated exactly by ≠ of 1(0(a)≠0(x)≠0(b)) expression or by 1(0(x)≠0(y)) expression, as well.

Your enunciation and the strange symbolism are the major ingredients in the recipe for the bowl of goulash you've been trying to serve.

No one claims that 0() is 1(), as no one claims that 0=1. If you organize the members of the set of real numbers in the ascending order, the result resembles a line. You claim that there are gaps in that set (collection), but you can't show that there is an interval [a,b] for which there is no real number xi.

Let xi be a real number -- a member of an ordered interval. What is the next real number?
Obviously, it is xi+1. But you claim that there are cases where xi has a successor xi+2. I suggested to you to hit the ordered set of positive integers and find the gaps in there, before trying to demolish R.

Let's see if you can get beyond shuffling 0()s and 1()s around: What is the immediate successor of √2? If the immediate successor is t, how do you find out that there should be a real number s right between √2 and t? This is the same as spotting a gap in 1,2,3_5,6... You can spot the gap only when you know how the missing number looks like, and if you know that, then the number exists. There is no way that there is any gap there, coz if i say let A be the set of positive integers, then I mean a set with no gaps. If I meant otherwise, I would included the provision in the definition.

So, what is the immediate successor of √2?

doronshadmi

14th October 2010, 05:01 PM

If you organize the members of the set of real numbers in the ascending order, the result resembles a line.

You are wrong.

The members of R set are 0(), and their distinct values can't be given without 1(), such that 1(0(x)≠0(y)), where 1() is exactly ≠ between distinct 0(x)≠0(y).

What is the immediate successor of √2?

It does not have an immediate successor exactly because no amount of distinct 0() is 1().

You still do not get the notion of infinite interpolation of distinct 0() along 1(0(x)≠0(y)), where x and y are distinct (x≠y) and order has no significance.

Your enunciation and the strange symbolism
It is strange because you don't get the notion of this notation.

epix

14th October 2010, 06:04 PM

The language that math speaks about a ≤ x ≤ b is based on collection of 0(), end exactly because a, x or b are no more than 0(), thay can't be 1(), which exists simultaneously at AND beyond the location of any given 0().

No, Doron. Numbers are not zero-dimensional objects; they are not points. We use numbers to locate points, that's all. There is a correspondence between numbers and points, though, but I'm not the one who will attempt the foolish feat of explaining.

Note the difference between F0()=0()LISH and FO=OLISH. Since O equals O, and O is the 15th letter of the alphabet, then 15=15 and so it's up to the "King Solomon" to right your mind.

I have written you quite boldly on some points, as if to remind you of them again, because of the grace God gave me.
Romans 15:15
http://www.jstor.org/pss/40248000

Religion & Philosophy
is like a car race and a trophy
first came Car and then came Race
as first comes God and then his Grace

(His Uttermost Omniscience God the Lord, Ph.D. shall try to explain regarding points. Well, let's hope for a miracle. :D)

jsfisher

14th October 2010, 09:09 PM

epix

15th October 2010, 12:04 AM

Ok, I'll admit it: Real life has distracted me from doronetics.

Can some one, please, explain what Doron means by his latest notational gibberish, 0() and 1()? I assume it has something to do with points and lines (Doron gets hung up on points and lines), but it isn't clear what it has to do with them. And it gets worse when Doron treats 0() and 1() as functions of boolean arguments.
God has taken a couple of days off, and so no one really knows what Doron means. But a guess could do as an interim: The 0() and 1() expressions are indigenous to Doronetics, coz parenthesis were invented to enclose characters -- characters such as 0 and 1. Since Doron's ideas are all of the novel kind, he puts the characters outside the parenthesis. There is a guess that says that () stands for an object and the prefix number translate the whole expression as 0() = "a zero-dimensional object" and 1() = " a one-dimensional object". The objects are presumably the point and the line.

There are instances where a lower-case letters have been spotted inside the parenthesis, such as 0(x). That expression probably reads zero-dimensional object x or point x. So a point in general is denoted as 0() and a particular point as 0(x). I haven't seen the line version yet for the particular case.

doronshadmi

15th October 2010, 05:31 AM

doronshadmi

15th October 2010, 05:35 AM

I haven't seen the line version yet for the particular case.

2(1(x)≠1(y))

In general X(x), where X is the dimensional space and x is a name of a given X.

doronshadmi

15th October 2010, 05:41 AM

No, Doron. Numbers are not zero-dimensional objects; they are not points. We use numbers to locate points,

In the case of R set, 0() is the minimal possible location along 1(), and no amount of 0() locations is 1(), because 1() is at AND beyond any given distinct 0() along it.

We use numbers to locate points
No, we use numbers whether thay are strict or non-strict, for example:

0() or 1() are strict numbers, where 0.999...[base 10]() is a non-strict number, such that no amount of the strict numbers
0()+0.9()+0.09()+0.009()+ ... is the strict number 1().

Also 1() or 2() are strict numbers, where 1.999...[base 10]() is a non-strict number, such that no amount of the strict numbers
1()+0.9()+0.09()+0.009()+ ... is the strict number 2().

...

etc. ... ad infinitum ...

Also be aware of the fact that, for example, 0.9(0(0.9)), where 0(0.9) is a strict location along 0.9(), and no amount of distinct 0() is 0.9().

epix

15th October 2010, 10:52 AM

Ok, I'll admit it: Real life has distracted me from doronetics.

Can some one, please, explain what Doron means by his latest notational gibberish, 0() and 1()? I assume it has something to do with points and lines (Doron gets hung up on points and lines), but it isn't clear what it has to do with them. And it gets worse when Doron treats 0() and 1() as functions of boolean arguments.

If you came across my attempt to decode that particular symbolism, then be advised to null and void it, coz Doron committed the defining here:
http://forums.randi.org/showpost.php?p=6444698&postcount=12016

According to his words, 0() and 1() stands for strict relation and non-strict relation respectively. So, the expression 1(0(x)≠0(y)) that he used quite recently means that the strict relation involving x is not identical to the strict relation involving y, and that is all happening in the non-strict relation 1(). He used that expression to show that 5/2, for example, doesn't have a real result. See, Doron keeps denying the existence of the linear continuum, and one of the consequences is that there exist non negative real numbers a and b with b≠0 where a/b doesn't have a real result. He can't provide an example of such two real numbers, though. Instead, he uses the strict and the non-strict arguments to show that such numbers do exist.

epix

15th October 2010, 11:18 AM

0() or 1() are strict numbers, where 0.999...[base 10]() is a non-strict number, such that no amount of the strict numbers
0()+0.9()+0.09()+0.009()+ ... is the strict number 1().

I thought that 0() stands for "strict relation" and 1() for "non-strict relation." That's how you defined the symbolism:

0() is for strict relation.

1() is for non-strict relation.

http://forums.randi.org/showpost.php?p=6444698&postcount=12016

Now you say that 0() and 1() are BOTH STRICT NUMBERS.
What happened to the strict and non-strict difference between 0() and 1() and how come that the word "number" suddenly replaced the original defining word "relation?"

Don't sweat it out to explain or you lose control over your gibberish for good.

But there is a tiny light at the end of the tunnel. I have an impression from your scribble that you don't agree with the idea that "0.999999..." actually equals 1. Am I right or not?

doronshadmi

15th October 2010, 11:43 AM

Now you say that 0() and 1() are BOTH STRICT NUMBERS.

EDIT:

0() or 1() are strict, where, for example, 0.999...[base 10]() is non-strict.

You still do not get X() as a measurement unite of existence, which can be strict or non-strict.

The same holds for some location w.r.t a given existence, for example:

0.999...[base 10](0(1)) means that there is a strict location 0(1) along the non-strict existence 0.999...[base 10]().

If 1() is considered w.r.t some given 0() along it in terms of location, then the location of 1() w.r.t 0() is non-strict, such that 1(0()).

Please do not mix between 1() as a strict number in terms of existence and 0(1) as a strict number in terms of location
under 1(0(1)), where 1() does not have a strict relation (in terms of location) w.r.t 0(1) and 0(1) has a strict relation (in terms of location) w.r.t 1().

But there is a tiny light at the end of the tunnel. I have an impression from your scribble that you don't agree with the idea that "0.999999..." actually equals 1. Am I right or not?

1(0.999...[base 10](0()))

You also have missed the logical aspect of 0(),1() as seen in http://forums.randi.org/showpost.php?p=6444698&postcount=12016.

doronshadmi

16th October 2010, 04:18 AM

Let us carefully look at the general form X(x).

X is the measurement of existence and x is the name of X under X', such that X'>X, where x is strict if X=0().

He can't provide an example of such two real numbers, though. Instead, he uses the strict and the non-strict arguments to show that such numbers do exist.

R set is the form 1(0(x)), such that x is strict (for example: x can be Pi, but it can't be 3.14…[base 10]).

Please do not mix between x and X because, for example, Pi(3.14…[base 10]()) or 1(0(Pi)) are valid, where 1(0(3.14…[base 10])) is invalid.

Non-strict x are defined under X>0.

epix

16th October 2010, 12:37 PM

It does not have an immediate successor exactly because no amount of distinct 0() is 1().

The reason why √2 doesn't have an "immediate" successor is that the line that models the set of real numbers is a collection of points whose number approaches infinity and there is no segment on that line that cannot correspond to a real number. This can be proven without inventing a strange symbolism, like 0() and 1().

Let s be the immediate successor of √2. In that case √2 < s with the consequnce of |√2 - s| > 0. That means |√2 - s| = m, where m is the length of a line segment. Since the length of a line segment can be divided by any positive real number except zero, it follows that

|√2 - s|/d = r

where d is any positive real number greater than 1. The consequence of such a division is

r < s

and therefore s cannot be the immediate successor to √2.

A proof by a contradiction such as that one was invented by the same species who also invented various pagan gods. That's why you try to invent other ways to proof stuff, so you would feel more "advanced."

doronshadmi

16th October 2010, 03:03 PM

A proof by a contradiction such as that one was invented by the same species who also invented various pagan gods. That's why you try to invent other ways to proof stuff, so you would feel more "advanced."
It is more advanced, because it discovers the fact that 1() is not a collection of 0(), where the proof by contradiction stays at the level of collection of 0().

epix

16th October 2010, 04:27 PM

It is more advanced, because it discovers the fact that 1() is not a collection of 0(), where the proof by contradiction stays at the level of collection of 0().

No, it's not advanced, coz it states among other things that a straight line cannot be fully covered by points. That means there exists a line segment A_____B on that line where there are no points between A and B. But since (B - A) > 0, the line segment has length m where m>0. There are many special points, and one of them is called "the mean," or the average. In this particular case, the average of A and B is

Pmean = m/2

A_____P_____B

Any line segment must have such a point. So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution. In other words, 6/2, for example, has indeterminable result -- the fraction does not equal 3. That, of course, doesn't apply in those happy moments when you cut salami to feed your face. LOL.

What? You don't cut salami? How come?

:jaw-dropp

Wow!

doronshadmi

17th October 2010, 12:08 AM

No, it's not advanced, coz it states among other things that a straight line cannot be fully covered by points. That means there exists a line segment A_____B on that line where there are no points between A and B. But since (B - A) > 0, the line segment has length m where m>0. There are many special points, and one of them is called "the mean," or the average. In this particular case, the average of A and B is

Pmean = m/2

A_____P_____B

Any line segment must have such a point. So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution. In other words, 6/2, for example, has indeterminable result -- the fraction does not equal 3. That, of course, doesn't apply in those happy moments when you cut salami to feed your face. LOL.

What? You don't cut salami? How come?

:jaw-dropp

Wow!

Under complex 1(0()) 0() is the minimal existing space of strict Locality, where 1() is the minimal existing space of strict Non-locality.

you can cut salami to infinitely many slides, which does not change the fact that 1(0(x)≠0(y)), such that ≠ is 1() at AND beyond 0(x) OR 0(y) upon infinitely many "cutting" levels.

Again, your notion is limited to the concept of collection of 0(), without understanding 1() as an existence that is at AND beyond 0(), as expressed by 1(0()).

doronshadmi

17th October 2010, 07:21 AM

So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution.
There are strict or non-strict solutions, for example:

Under 1(0.999...[base 10]()), 1()-0.999...[base 10]() = 0.000...1[base 10](), where 0.000...1[base 10]() is a non-strict solution,
and 0.999...[base 10]()+0.000...1[base 10]() = 1(), where 1() is a strict solution.

jsfisher

17th October 2010, 10:47 AM

0() is for strict relation....

A simple, "No, I can't explain them," would have sufficed. No need for gibberish.

doronshadmi

17th October 2010, 12:10 PM

A simple, "No, I can't explain them," would have sufficed. No need for gibberish.

A simple, "No, I can't get them," would have sufficed. No need for your gibberish-loop.

The Man

17th October 2010, 12:15 PM

"≠" is exactly the non-local property of 1() w.r.t any 0(x),0(y), such that 1(0(x)≠0(y)).

Still does not make it a location on a line, let alone a location(s) on a line that is not or can not be covered by point(s)

How about you first learn things beyond your 0() only reasoning?

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

The Man

17th October 2010, 12:22 PM

Ok so you can’t actually get novell notions about those papers.

Again Doron, you simply not understanding those papers does not constitute any "novell notions about those papers".

epix

17th October 2010, 12:28 PM

There are strict or non-strict solutions, for example:

Under 1(0.999...[base 10]()), 1()-0.999...[base 10]() = 0.000...1[base 10](), where 0.000...1[base 10]() is a non-strict solution,
and 0.999...[base 10]()+0.000...1[base 10]() = 1(), where 1() is a strict solution.
Why do you include the number base in there? :confused:

Even without it, there is a strong impression that subtraction yields "non-strict solutions," and addition yields "strict solutions," which not what you intended.

You don't relate the operands well: the expression "0.999..." implies a number where the decimal digits repeat infinitely, whereas the result "0.000...1" implies a very small but finite number. So the subtraction 1 - 0.999... = 0.000...1 is not a good rendition of the idea of non-strictness.

The "obsolete" math uses this syntax:

1 - (1 - 1/10n) where n → ∞.

The result is then

1 - (1 - 1/10n) = 1 - 1 + 1/10n = 1/10n where n → ∞

and there is no doubt about what is meant.

doronshadmi

17th October 2010, 12:56 PM

doronshadmi

17th October 2010, 01:04 PM

whereas the result "0.000...1" implies a very small but finite number.

Wrong.

0.000...1 is an example of non-strict (infinitely smaller AND > 0) number.

You still miss the notion of infinite interpolation.

The Man

17th October 2010, 01:08 PM

Ok, let us continue to develop OM.

The following diagram demonstrates the notion of nested levels of existence among Non-Locality\Locality Linkage, where the tangent line between each pair of quarter circles represents The Non-locality of a given nested level, and 0() represents the "depth" of Locality w.r.t to Non-Locality, for any given nested level:

http://farm5.static.flickr.com/4147/5089991451_9b8ccd7ee1_z.jpg

This model can be used to understand better the differences between microscopic or macroscopic black holes.

You can make up as much nonsensical gibberish, drawings and notations as you want Doron, but until you make you "OM" both self-consistent and generally consistent you haven't even started to "develop OM".

We are still waiting for you to identify any locations on a line that are not or can not be covered by points.

doronshadmi

17th October 2010, 01:20 PM

Still does not make it a location on a line,

Location along 1() is exactly 0().

Since you get 1() only in terms of 0(), your 0()-only reasoning can't comprehend the fact that 1() is at AND beyond any given 0() along 1().

As a result you do not understand the non-local property of ≠ w.r.t any given pair of 0() localities.

doronshadmi

17th October 2010, 01:25 PM

You can make up as much nonsensical gibberish, drawings and notations as you want Doron, but until you make you "OM" both self-consistent and generally consistent you haven't even started to "develop OM".

We are still waiting for you to identify any locations on a line that are not or can not be covered by points.

I am not with you in your 0()-only game.

Actually I do not care anymore about your 0()-only replies.

The Man

17th October 2010, 01:36 PM

Location a long 1() is exactly 0().

"≠" still isn't a location.

Are you claiming that any location “a long 1() is exactly” a point?

Since you get 1() only in terms of 0(), your 0()-only reasoning can't comprehend the fact that 1() is at AND beyond ant given 0() along 1().

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Oh and evidently you simply can’t understand that a line segment is specifically not “beyond” its given end points and in the case of segment represented by an interval like (1,2) the line segment isn’t even “at” those two points.

As a result you do not understand the non-local property of ≠ w.r.t any given pair of 0() localities.

You still simply don’t understand that "≠" still isn't a location and “As a result” your “non-local property of ≠ w.r.t any given pair of 0() localities.” is still simply just nonsense.

The Man

17th October 2010, 01:39 PM

I am not with you in your 0()-only game.

Actually I do not care anymore about your 0()-only replies.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

epix

17th October 2010, 01:49 PM

Wrong.

0.000...1 is an example of non-strict (infinitely smaller AND > 0) number.

So why did you use 1 - 0.999... instead of 1 - 0.999...9?

I think that the old-fashioned expression 10-n (n → ∞) is superior in clarity to your version 0.000...1.

The Man

17th October 2010, 02:02 PM

Because all of Doron’s notions and notations are, well, “non-strict”, Epix (especially when it comes to Doron’s application of them).

epix

17th October 2010, 02:14 PM

http://farm5.static.flickr.com/4147/5089991451_9b8ccd7ee1_z.jpg

This model can be used to understand better the differences between microscopic and macroscopic non-rotating black holes.

:confused:

Are you sure?

I've seen models like that, (http://www.realhomepage.de/members/kevinschuetz/AnnaKournikovaBikiniThongStringAssButtStjrtRumpaAK 08.jpg) but there was never any cosmology issue near by.

What size is that 1(0.8... anyway?

The Man

17th October 2010, 02:37 PM

:confused:

Are you sure?

I've seen models like that, (http://www.realhomepage.de/members/kevinschuetz/AnnaKournikovaBikiniThongStringAssButtStjrtRumpaAK 08.jpg) but there was never any cosmology issue near by.

What size is that 1(0.8... anyway?

Perhaps he has a different "OM" meaning for "black hole" as well (at least the “non-rotating” ones anyway)?

doronshadmi

18th October 2010, 12:50 AM

You still simply don’t understand that "≠" still isn't a location and “As a result” your “non-local property of ≠ w.r.t any given pair of 0() localities.” is still simply just nonsense.
What you say is disjoint from your understanding.

For example, you do not get that your claim that "≠" is not a location is equivalent to the claim that "≠" is non-local, and indeed ≠ is the non-locality of 1() w.r.t any distinct 0() along it, such that 1() is at AND not at w.r.t any given distinct 0().

doronshadmi

18th October 2010, 12:53 AM

Because all of Doron’s notions and notations are, well, “non-strict”, Epix (especially when it comes to Doron’s application of them).
Because all of The Man's notions and notations are, well, “strict”-only, he can't get non-strict notions or notations.

doronshadmi

18th October 2010, 12:57 AM

I've seen models like that, (http://www.realhomepage.de/members/kevinschuetz/AnnaKournikovaBikiniThongStringAssButtStjrtRumpaAK 08.jpg) but there was never any cosmology issue near by.
epix, you can be happy by aware of the fact that I've seen models like that, (http://www.realhomepage.de/members/kevinschuetz/AnnaKournikovaBikiniThongStringAssButtStjrtRumpaAK 08.jpg) and you are made of space\time stars dust.

doronshadmi

18th October 2010, 01:49 AM

What size is that 1(0.8... anyway?
You can use ant measurement unit, but it does not change the fact that the measurement is done under Non-locality\Locality Linkage.

doronshadmi

18th October 2010, 02:20 AM

So why did you use 1 - 0.999... instead of 1 - 0.999...9?
You can use 0.999...9 instead of 0.999... as long as "..." is understood as infinite interpolation, such that both numbers < 1 by 0.000...1

I think that the old-fashioned expression 10-n (n → ∞) is superior in clarity to your version 0.000...1.
The old-fashioned expression is not fine enough in order to distinguish between, for example,
0.000...1[base 2] as the complement of 0.111...[base 2] to 1, or 0.000...1[base 3]as the complement of 0.222...[base 3] to 1, as seen in:

http://farm3.static.flickr.com/2793/4318895416_e5d2042b0c_z.jpg?zz=1

doronshadmi

18th October 2010, 06:08 AM

Oh and evidently you simply can’t understand that a line segment is specifically not “beyond” its given end points and in the case of segment represented by an interval like (1,2) the line segment isn’t even “at” those two points.

The 1() space is exactly at AND not at any considered distinct 0().

In the case of (1,2) 0(1) OR 0(2) are simply not considered, so?

epix

18th October 2010, 10:12 AM

Originally Posted by epix
I think that the old-fashioned expression 10-n (n → ∞) is superior in clarity to your version 0.000...1.

The old-fashioned expression is not fine enough in order to distinguish between, for example,
0.000...1[base 2] as the complement of 0.111...[base 2] to 1, or 0.000...1[base 3]as the complement of 0.222...[base 3] to 1, as seen in:

http://farm3.static.flickr.com/2793/4318895416_e5d2042b0c_z.jpg?zz=1

What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2-n where n → ∞ equals 0.1111... [base 2]

The Man

18th October 2010, 03:42 PM

What you say is disjoint from your understanding.

No Doron, it isn't.

For example, you do not get that your claim that "≠" is not a location is equivalent to the claim that "≠" is non-local, and indeed ≠ is the non-locality of 1() w.r.t any distinct 0() along it, such that 1() is at AND not at w.r.t any given distinct 0().

So now you agree that "≠" is not a location on a line?

You still haven’t answered this question.

Are you claiming that any location “a long 1() is exactly” a point?

Again, please indentify any location on a line that is not and can not be covered by points.

Because all of The Man's notions and notations are, well, “strict”-only, he can't get non-strict notions or notations.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

The 1() space is exactly at AND not at any considered distinct 0().

Once again, your contradictory claim, thus “exactly” and only your problem.

In the case of (1,2) 0(1) OR 0(2) are simply not considered, so?

So, it simply demonstrates once again that you have no idea what you are talking about. “In the case of (1,2)” both those point are “considered” specifically as the boundaries. What they are specifically “not considered”, however, is members of the set of points that result from that interval. Not included in the set does not mean or even infer that they “are simply not considered”, but given your “magnitude of existence” nonsense that seems a fact that you have “simply not considered”.

epix

18th October 2010, 04:51 PM

epix, you can be happy by aware of the fact that I've seen models like that, (http://www.realhomepage.de/members/kevinschuetz/AnnaKournikovaBikiniThongStringAssButtStjrtRumpaAK 08.jpg) and you are made of space\time stars dust.

Tell Henry to leave me alone. (http://handheld-vacuumcleaners.com/wp-content/uploads/2008/11/henry-vacuum-cleaner.jpg) I'm taking the train to Suffragette City tomorrow.

doronshadmi

18th October 2010, 11:33 PM

So now you agree that "≠" is not a location on a line?
Now I agree that ≠ is the non-locality of 1() w.r.t any given distinct 0() along it, such that 1() is at AND not at the given distinct 0().

Again, please indentify any location on a line that is not and can not be covered by points.
You simply can't get anything beyond distinct 0(), isn't it The Man?

Again, stop simply trying to posit aspects of your own failed reasoning onto others.
Again, stop simply trying to posit aspects of your 0()-only reasoning onto others.

Once again, your contradictory claim, thus “exactly” and only your problem.
Once again, your contradictory claim is derived from your 0()-only reasoning, thus “exactly” and only your problem.

So, it simply demonstrates once again that you have no idea what you are talking about. “In the case of (1,2)” both those point are “considered” specifically as the boundaries.
Nonsense, (1,2) means, for example, that 1((0(1)+0.000...1())≠(0(2)-0.000...1()))

What they are specifically “not considered”, however, is members of the set of points that result from that interval. Not included in the set does not mean or even infer that they “are simply not considered”, but given your “magnitude of existence” nonsense that seems a fact that you have “simply not considered”.
No The Man, your 0()-only reasoning is too weak in order to understand expressions like (0(1)+0.000...1()) or (0(2)-0.000...1()), and how ≠ is exactly the non-locality of 1() between them.

doronshadmi

18th October 2010, 11:45 PM

What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2-n where n → ∞ equals 0.1111... [base 2]
n-n is a general form, but it can't be used for fine distinction, for example:

0.111...[base 2] (which is under 2-n) ≠ 0.111...[base 3] (which is under 3-n), as can be seen in:

http://farm5.static.flickr.com/4103/5096227808_e362e07fe9_z.jpg

It is clear that (1 - 0.1111...[base 2]) ≠ (1 - 0.1111...[base 3])

doronshadmi

19th October 2010, 01:10 AM

Tell Henry to leave me alone. (http://handheld-vacuumcleaners.com/wp-content/uploads/2008/11/henry-vacuum-cleaner.jpg) I'm taking the train to Suffragette City tomorrow.

So be aware of black holes when you are on the railroad.

zooterkin

19th October 2010, 04:52 AM

You don't relate the operands well: the expression "0.999..." implies a number where the decimal digits repeat infinitely, whereas the result "0.000...1" implies a very small but finite number. So the subtraction 1 - 0.999... = 0.000...1 is not a good rendition of the idea of non-strictness.

We've been round this one a few times before with Doron. He thinks that
1 / 3 * 3 = 0.999...
and that this is not equivalent to 1. So, he invented the 0.000...1 notation, and thinks it means something profound.

doronshadmi

19th October 2010, 05:02 AM

We've been round this one a few times before with Doron. He thinks that
1 / 3 * 3 = 0.999...
and that this is not equivalent to 1. So, he invented the 0.000...1 notation, and thinks it means something profound.
No zooterkin, you wrongly think that the strict number 1/3 is the non-strict number 0.333...[base 10].

You are also missing http://forums.randi.org/showpost.php?p=6451665&postcount=12034.

The Man

19th October 2010, 02:58 PM

Now I agree that ≠ is the non-locality of 1() w.r.t any given distinct 0() along it, such that 1() is at AND not at the given distinct 0().

Agree with whom, yourself? That you claim it "is at AND not at the given distinct 0()" shows that you can't even agree with yourself.

You simply can't get anything beyond distinct 0(), isn't it The Man?

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Again, stop simply trying to posit aspects of your 0()-only reasoning onto others.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Once again, your contradictory claim is derived from your 0()-only reasoning, thus “exactly” and only your problem.

What contradictory claim of mine are you referring to?

Nonsense, (1,2) means, for example, that 1((0(1)+0.000...1())≠(0(2)-0.000...1()))

Nope, as explained to you many times before it means specifically that the boundary points are not included in the set of points resulting from that interval.

No The Man, your 0()-only reasoning is too weak in order to understand expressions like (0(1)+0.000...1()) or (0(2)-0.000...1()), and how ≠ is exactly the non-locality of 1() between them.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

“≠” is still not a location on a line.

Again, please indentify any location on a line that is not and can not be covered by points.

epix

19th October 2010, 05:34 PM

Originally Posted by epix
What do you mean? The expression is universal; it applies to all number bases. For example

1 - 2^-n where n → ∞ equals 0.1111... [base 2]

n-n is a general form, but it can't be used for fine distinction, for example:

0.111...[base 2] (which is under 2-n) ≠ 0.111...[base 3] (which is under 3-n), as can be seen in:

http://farm5.static.flickr.com/4103/5096227808_e362e07fe9_z.jpg

It is clear that (1 - 0.1111...[base 2]) ≠ (1 - 0.1111...[base 3])

I never mentioned n-n. Where do you see it?

I mentioned a formula particular to base 2, where I meant by "universal" the involvement of the limit, that means n → ∞. It wasn't exactly the way I should have explained it, so that's why you tried to say that 1 - 2-n where n → ∞ doesn't apply to other number bases apart from base 2. So I need to make amends.

The universal formula that involves the limit n → ∞ and applies to all number bases is

(an - 1)/(an+1 - an) = 0.1111... [base a]

where n → ∞ and a is the number base. You can substitute finite k for n and run a few examples.

epix

19th October 2010, 06:00 PM

No zooterkin, you wrongly think that the strict number 1/3 is the non-strict number 0.333...[base 10].

Why do you feel the need for changing the traditional description? 1/3 is the "exact form" and 0.333... is called the "approximate form." Believe it or not, the distinction have had its own description.

doronshadmi

20th October 2010, 05:21 AM

Agree with whom, yourself? That you claim it "is at AND not at the given distinct 0()" shows that you can't even agree with yourself.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

What contradictory claim of mine are you referring to?

Nope, as explained to you many times before it means specifically that the boundary points are not included in the set of points resulting from that interval.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

“≠” is still not a location on a line.

Again, please indentify any location on a line that is not and can not be covered by points.
The Man, enjoy your 0-only reasoning.

doronshadmi

20th October 2010, 05:47 AM

Why do you feel the need for changing the traditional description? 1/3 is the "exact form" and 0.333... is called the "approximate form." Believe it or not, the distinction have had its own description.

1/3=0.333...[base 10] by the traditional description, and it is false.

doronshadmi

20th October 2010, 06:13 AM

I never mentioned n-n. Where do you see it?

I mentioned a formula particular to base 2, where I meant by "universal" the involvement of the limit, that means n → ∞. It wasn't exactly the way I should have explained it, so that's why you tried to say that 1 - 2-n where n → ∞ doesn't apply to other number bases apart from base 2. So I need to make amends.

The universal formula that involves the limit n → ∞ and applies to all number bases is

(an - 1)/(an+1 - an) = 0.1111... [base a]

where n → ∞ and a is the number base. You can substitute finite k for n and run a few examples.
You can play with the notations as much as you like, but it does not change the fact that, for example: 1 - 0.111...[base 2]=0.000...1[base 2], or 1-0.999...[base 10]=0.000...1[base 10], where 0.000...1[base 10] < 0.000...1[base 2].

You are also missing http://forums.randi.org/showpost.php?p=6451665&postcount=12034.

sympathic

20th October 2010, 10:43 AM

epix

20th October 2010, 10:51 AM

1/3=0.333...[base 10] by the traditional description, and it is false.

The equality between the exact and the approximate form 1/3 = 0.333... doesn't disprove the existence of a number where the decimal digit 3 repeats itself the way that the number of repetitions approaches infinity. The approximate form is used to display the final result, but it never enters any algebraic manipulation. You can see expressions, such as (1/3)2 but never (0.333...)2.

It's the same case with Pi = 3.1415... with the difference that you won't be able to trace the "complementary digit" of Pi, coz it is an irrational number. You can use your notation that says

0.999... + 0.000...1 = 1

but your notation cannot solve

3.1415... + 0.000...x = Pi

to "prove" anything. That's why the approximate form is never used in algebraic manipulations, coz 0.000...x is vastly inconsistent and cumbersome expression. You can use your notation as an argument that can be followed only with rational numbers, but it doesn't work with the irrational numbers. That's why jpfisher always says that your stuff is inconsistent and can't cover all the classes.

epix

20th October 2010, 11:22 AM

He still does not get that "...." means infinite times, and "0.0......1" is just something you can type but does not exist in reality.
He is using the recurrence

0.9 + 0.1 = 1
0.99 + 0.01 = 1
0.999 + 0.001 = 1
.
.
.
0.999... + 0.000...1 = 1

to demonstrate that 0.999... doesn't equal 1. There has been a great deal of confusion regarding the usage and the interpretation of the term "0.999..." as it can be seen here:
http://www.mathforum.org/dr.math/faq/faq.0.9999.html

epix

20th October 2010, 01:09 PM

You can play with the notations as much as you like, but it does not change the fact that, for example: 1 - 0.111...[base 2]=0.000...1[base 2], or 1-0.999...[base 10]=0.000...1[base 10], where 0.000...1[base 10] < 0.000...1[base 2].

You are also missing http://forums.randi.org/showpost.php?p=6451665&postcount=12034.
You are trying to prove something using a notation the meaning of which you don't understand well and that you call a "non-strict number," which means an "approximate form" in the traditional language. You are not familiar with the usage and interpretation of the approximate form.

Have you ever seen an expression, such as e4 F?

You didn't, coz a thermometer scale cannot accommodate all possible exact results of various computations, such as f(x) = e4. Instead, an analogue thermometer scale is divided into equidistant segments and the points are marked with decimal numbers. That means a meteorologist needs to convert the exact form e4 into its approximate form, which is 54.598... to see if the temperature obtained by some formula is above or bellow the point of freezing.

The approximate form is necessary for scientific applications of math, and, as such, it's not a subject to any inquiries that concerns math itself.

The approximate form is used in computational devices, coz scientists use computers and calculators. The devices do the internal math in binary numbers and can't possibly handle any exact computations. So there is an agreement that when the result shows 0.111111111111, for example, it is equivalent to the exact form 1/9 The same goes for informal numerical definition in some math texts, such as x = 0.111..., where the expression implies that x is approaching the limit 1/9; it doesn't indicate number 10-1 + 10-2 + 10-3...

You are trying to find a pointless line segment using . . . well, pointless arguments.

epix

20th October 2010, 01:44 PM

The Man, enjoy your 0-only reasoning.
:confused:

"Well, your fingers weave quick minarets
Speak in secret alphabets..." (http://www.reinehr.be/doors/morrisonhotel_bestanden/image001.jpg)

Well, your fingers weave quick minarets, speak in secret alphabets... (http://www.skiresortshotels.com/guide/images/hotels/nh-doron/nh-doron_exterior1.jpg)

epix

21st October 2010, 01:49 AM

You are also missing http://forums.randi.org/showpost.php?p=6451665&postcount=12034.
The reason why I might miss something is that you are missing stuff in the first place:

0.000...1 is an example of non-strict (infinitely smaller AND > 0) number.

I expect that the subordinating conjunction "than" shows up after "infinitely smaller," but big, fat "AND" sits there instead. "Infinitely smaller AND?" It should read Infinitely smaller than [something] AND greater than zero, coz you using AND as a Boolean operator. Or did you attempt to write Infinitely small AND greater than zero? Just make up your mind what you want to say and then make sure that stuff isn't missing from your sentences, otherwise the chances that someone would understand what you mean are infinitely small BUT > 0.

doronshadmi

21st October 2010, 04:46 AM

He still does not get that "...." means infinite times, and "0.0......1" is just something you can type but does not exist in reality.
You still do not get that 0.000...1 is a result of the irreducibility of 1-dim space to 0-dim space.

doronshadmi

21st October 2010, 05:03 AM

3.1415... + 0.000...x = Pi

to "prove" anything. That's why the approximate form is never used in algebraic manipulations, coz 0.000...x is vastly inconsistent and cumbersome expression.
Again epix, you simply can't comprehend that, for example, 1-dim space is irreducible to 0-dim space, which leaves a room for non-strict numbers, which are the results of 1-0.111...[base 2], 1-0.999...[base 10], or PI-3.14...[BASE 10], etc. ... ad infinitum.

The rest of your posts, are based on this miss-comprehension.

doronshadmi

21st October 2010, 05:10 AM

The reason why I might miss something is that you are missing stuff in the first place:

I expect that the subordinating conjunction "than" shows up after "infinitely smaller," but big, fat "AND" sits there instead. "Infinitely smaller AND?" It should read Infinitely smaller than [something] AND greater than zero, coz you using AND as a Boolean operator. Or did you attempt to write Infinitely small AND greater than zero? Just make up your mind what you want to say and then make sure that stuff isn't missing from your sentences, otherwise the chances that someone would understand what you mean are infinitely small BUT > 0.

"Infinitely smaller AND > 0" means that given any arbitrary (0,1] number, the considered number
is always smaller than the given arbitrary (0,1] number AND > 0.

The Man

21st October 2010, 06:56 AM

"Infinitely smaller AND > 0" means that given any arbitrary (0,1] number, the considered number
is always smaller than the given arbitrary (0,1] number AND > 0.

Not for the interval you indicated, a 1 is included in that interval. So while 1 > 0 it is not smaller than, well, 1. The interval should have been (0,1) thus any arbitrary number included in that interval is > 0 and < 1.

The Man

21st October 2010, 07:10 AM

The Man, enjoy your 0-only reasoning.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

For example we can represent the resulting set from the interval (2,6] as a union of resulting sets from the half closed intervals (2,3], (3,4], (4,5] and (5,6]. The “0-only reasoning” you refer to is still only yours, so stop simply trying to attribute it to others.

By the way, have you identified that location or locations on a line that you claim are not covered by points?

doronshadmi

21st October 2010, 08:02 AM

Let us take for example PI.

PI > than any non-strict number that is defined by the place value method.

For example, 11.00100100001111110110101010001000100001011010001 10000100011010011...[base 2] < PI , where 11.0010...[base 2] < PI first 6 scale levels are clearly seen by the following diagram:
http://farm2.static.flickr.com/1394/5101820741_6cae70c3c9_b.jpg
The bold horizontal black 1-dim element is PI.

The orange rectangle is unit 1, which is common to any given [base n>1] number system.

The purple objects are the [base 2] number system.

The vertical green line is the exact location of PI on 1-dim space, and it is clearly seen that 11.0010...[base 2] < PI and this fact is not changed upon infinitely many scale levels.

(The black numbers and the thin lines are [base 10] number system, which is different than [base 2] number system, but it is also < PI).

zooterkin

21st October 2010, 08:13 AM

Let us take for example PI.

It's 'pi' or 'Pi', not 'PI'.

PI > than any non-strict number that is defined by the place value method.

Really? Did you mean to say that?

doronshadmi

21st October 2010, 08:13 AM

Not for the interval you indicated, a 1 is included in that interval. So while 1 > 0 it is not smaller than, well, 1. The interval should have been (0,1) thus any arbitrary number included in that interval is > 0 and < 1.
Some reading problems?

The considered number is smaller than any arbitrary number of (0,1] AND it is also > 0.

In other words, this considered number is not 1 AND it is not 0.

doronshadmi

21st October 2010, 08:18 AM

It's 'pi' or 'Pi', not 'PI'.
pi or Pi already used bi the wrong notion that the place value is Pi or pi.

So I use PI as the exact location on 1-dim space, which is > any place value system.

Really? Did you mean to say that?
Yes I do mean to say that!

readme.txt

21st October 2010, 10:45 AM

http://en.wikipedia.org/wiki/0.999...#Skepticism_in_education

Skepticism in education

Students of mathematics often reject the equality of 0.999... and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:
Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[35]
Some students interpret "0.999..." (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".[36]
Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999..." as meaning the sequence rather than its limit.[37]

Just sayin'

epix

21st October 2010, 11:17 AM

You still do not get that 0.000...1 is a result of the irreducibility of 1-dim space to 0-dim space.

Doron, you are building a humongous press to crack a walnut. A math reduction is accomplished by two common arithmetic operations: subtraction and division. The applicable difference is:

Subtraction: a - x = 0
Division: a/x = 0

Solve both equations and you find out that your concept of irreducibility crumbles under the hard friction that an eraser can cause onto your 1-dim space, but in the case of division, a trace of that 1-dim space always survives the vicious attack. That's because when you start to erase the word DIVIDE from the end and reduce it up to DIVI, a miracle takes place and DIVI becomes a full word again with the same cardinality reading "DIVIne." Some of us enjoy a divine protection and so does 1-dim space. That's why the solution to

a/x = 0

doesn't exist for a > 0, and you can't therefore reduce 1-dim space to 0-dim space by using division.

The divide/divine protection was used in the attempt to reduce a NUMBER (of people). The reduction came to a halt when NUMBER was reduced to NU and became divided into N:U. Since N=14 and U=21 in the alphabet, N:U = 14:21, so you can use 14:21 to find the practical example of the divine/divide protection:

Then Moses stretched out his hand over the sea, and all that night the LORD drove the sea back with a strong east wind and turned it into dry land. The waters were divided.
Exodus 14:21

See? If it wasn't for His Uttermost Omniscience God the Lord, Ph.D., you would be now sitting in Cairo, Egypt making $0.000...1 an hour.

epix

21st October 2010, 12:08 PM

http://en.wikipedia.org/wiki/0.999...#Skepticism_in_education

Just sayin'
What are you saying? If you're saying that the kids got confused by idiotic symbolism that is strongly counterintuitive, then you are right.

readme.txt

21st October 2010, 12:16 PM

What are you saying? If you're saying that the kids got confused by idiotic symbolism that is strongly counterintuitive, then you are right.

Not only the kids, I'd say. Pseudomathematicians too.

epix

21st October 2010, 01:27 PM

Not only the kids, I'd say. Pseudomathematicians too.
Pseudomathematicians invented the symbolism out of their laziness. 0.999... simply implies a number whose fractional part comprise 9's the number of which approaches infinity. When 1, 2, 3, 4, ... shows up, no one talks any limits, so why should things be different with 0.999...?

epix

21st October 2010, 02:32 PM

doronshadmi

22nd October 2010, 03:10 AM

Here is an example of the fact that we may not see every arrangement there is, coz we can't be "omnifocused."

Doron, [text]

So you began to write a short letter/post to Doron. The nature of the text depends on what you want to say and the name that you've already written doesn't affect the composition of the text. But it can. Doron makes often ascriptions that are not immediately clear and here is a model of such.

Doron, 14_5

Assuming that the numerical assignment isn't random, the possible logical explanation to the choice of the numbers is that it applies to the last letter in the name: N is the 14th letter in the alphabet and the 5th one in the name. So substitute "text" in the brackets with both numbers:

Doron, [14_5]

Now you respond in kind. Would Doron be able to decode the symbolism, which says to look for a sentence that is made of 14 words where 5 of them include letter N? If he does, would you be able to compose such a sentence given the numerical restriction?

Wow! That was fast.

;)

Epix, Traditional Math takes the palace value system as one of many methods of numerals' representation.

By following this notion, a numeral is not the number itself, so according this notion anyone who claims that, for example, the numeral 0.999… is smaller than the number [B]1, simply shows (according Traditional Math) that he\she can't distinguish between the representation (place value method, in this case) and the represented (the number itself).

By following Traditional Math 1 = 0.999…[base 10] = …= 0.111…[base 2] , where in this case "=" simply says that number 1 has many representations that are numerals, where no numeral is actually the number 1 itself.

As long as Traditional Math understands the place value system as a representation method out of many other representations' methods, there can't be any dialog between OM (which claims that the place value is a system of numbers) and Traditional Math.

doronshadmi

22nd October 2010, 04:52 AM

Take for example this part, taken from http://en.wikipedia.org/wiki/Number :

When a real number represents a measurement, there is always a margin of error. This is often indicated by rounding or truncating a decimal, so that digits that suggest a greater accuracy than the measurement itself are removed. The remaining digits are called significant digits. For example, measurements with a ruler can seldom be made without a margin of error of at least 0.01 meters. If the sides of a rectangle are measured as 1.23 meters and 4.56 meters, then multiplication gives an area for the rectangle of 5.6088 square meters. Since only the first two digits after the decimal place are significant, this is usually rounded to 5.61

For example, number PI itself (which is not a Q member) can't be accuratly defined by place value mathod, which is alwasy based of collections of equale sizes upon infinitely many given scale levels (which is a property of Q members).

Such fractals simply can't define the accurate value of PI, as clearly seen in http://forums.randi.org/showpost.php?p=6465716&postcount=12075 example.

But since Traditional Math understands the place value method as a system of numerals, it does not have any problem to use an expression like number "PI = numral 3.14...", where "=" in this case means: "represented by ...".

------------------------------

OM is developed beyond the notions of Traditional Math about the concept of Number, and shows that the concept of Number of Traditional Math is the particular case of a collection of distinct 0() spaces on 1() space, where any given distinct 0() space is local w.r.t 1() space, and 1() space is non-local w.r.t any given distinct 0() space.

This novel notion is expressed by 1(0()), which is based on the novel notion of different levels of existence between fullness (that has no successor) and emptiness (that has no predecessor), so 1(0()) is actually under the following framework:

∞[B](
1(0())
)

readme.txt

22nd October 2010, 06:27 AM

Pseudomathematicians invented the symbolism out of their laziness. 0.999... simply implies a number whose fractional part comprise 9's the number of which approaches infinity. When 1, 2, 3, 4, ... shows up, no one talks any limits, so why should things be different with 0.999...?

I don't get why it is "laziness", but well, that's not really important. And I know 0.9(bar) = 0.999... = 1. That's for sure. I'm just saying only pseudomathematicians or kids/students say it's not.

I'm not here for the whole "Deeper than primes" debate (because I didn't read it and I'm still wondering what this is all about), I'm here for the 0.9(bar) = 1 debate.

P.S. Why is this thread in the "Religion" subforum?

zooterkin

22nd October 2010, 06:41 AM

P.S. Why is this thread in the "Religion" subforum?

It's "Philosophy"; well, it certainly isn't mathematics.

readme.txt

22nd October 2010, 07:50 AM

It's "Philosophy"; well, it certainly isn't mathematics.

Really? But I read some maths here and there. How is it philosophy?

doronshadmi

22nd October 2010, 08:33 AM

Really? But I read some maths here and there. How is it philosophy?

Hi readme.txt,

This thread is here exactly because of what you say:

And I know 0.9(bar) = 0.999... = 1. That's for sure. I'm just saying only pseudomathematicians or kids/students say it's not.

For better understanding, please look at:

http://forums.randi.org/showpost.php?p=6468807&postcount=12085

http://forums.randi.org/showpost.php?p=6469003&postcount=12086

doronshadmi

22nd October 2010, 10:41 AM

Let's show the first 7 levels of the non-strict number 3.141592 … < PI.

http://farm5.static.flickr.com/4086/5105470874_17e5aaa5f3.jpg

http://farm2.static.flickr.com/1256/5105473512_aa49164260.jpg

http://farm2.static.flickr.com/1390/5104877745_f8f2627061.jpg

http://farm2.static.flickr.com/1086/5105473650_5aaa36b4b5.jpg

http://farm5.static.flickr.com/4085/5105473724_9ee904f365.jpg

http://farm2.static.flickr.com/1093/5104877951_6cb1bafc28.jpg

http://farm2.static.flickr.com/1073/5104878019_3bfda7675c.jpg

PI is shown by the green vertical line, and it is clear that 3.14…[base 10] < PI even if there are infinitely many places after the redix point (http://en.wikipedia.org/wiki/Radix_point).

The reason is very simple:

The place value system is based on equal sizes that exist upon infinitely many scale levels, and such a system simply can't be an accurate measurement tool of any irrational number.

But Traditional Mathematics does not care about this fact, because according to its notion, the place value method is no more than a numeration (some representation technique, out of many other representations) and not the number itself.

------------------------------

Again,

OM is developed beyond the notions of Traditional Math about the concept of Number, and shows that the concept of Number of Traditional Math is the particular case of a collection of distinct 0() spaces on 1() space, where any given distinct 0() space is local w.r.t 1() space, and 1() space is non-local w.r.t any given distinct 0() space.

This novel notion is expressed by 1(0()), which is based on the novel notion of different levels of existence between fullness (that has no successor) and emptiness (that has no predecessor), so 1(0()) is actually under the following framework:

∞[B](
1(0())
)

epix

22nd October 2010, 12:18 PM

I don't get why it is "laziness", but well, that's not really important. And I know 0.9(bar) = 0.999... = 1.

The reason why you "know" that 0.999... = 1 is simple:

Many are persuaded by an appeal to authority from textbooks and teachers...

The symbolic rendition 0.999... = 1 is a short of the full representation that starts bellow:

0.999... = (10n - 1)/10n where n → ∞.

When you substitute n in the formula with 1, 2, 3, 4, the result is 0.9, 0.99, 0.999, 0.9999 respectively. Obviously, substituting n with positive integer that approaches infinity results in a number that can be rendered as 0.999.... The ellipses indicate that the 9's will repeat ad infinitum. This number is always smaller than 1, but . . .

lim[n → ∞] (10n - 1)/10n = 1

The above identity says that the limit of the expression equals 1; it doesn't say that in some moment, as n approaches infinity, 0.999... suddenly becomes identical to integer 1. But in practical applications, such as in calculus, various limits are treated as an exact representation of the results that involve numbers that are approaching certain values through a convergence, but never reach them. The margin of error is simply "infinitely small", and can be safely neglected. No one ever went wrong by doing so.

There are surely kids out there who now believe that 0.999... as a number where the 9s repeat infinitely doesn't simply exist and that Doron has been right after all saying that a straight line has "blind spots" -- that there are segments on that line that cannot be covered by points.

doronshadmi

22nd October 2010, 01:43 PM

The reason why you "know" that 0.999... = 1 is simple:

The symbolic rendition 0.999... = 1 is a short of the full representation that starts bellow:

0.999... = (10n - 1)/10n where n → ∞.

When you substitute n in the formula with 1, 2, 3, 4, the result is 0.9, 0.99, 0.999, 0.9999 respectively. Obviously, substituting n with positive integer that approaches infinity results in a number that can be rendered as 0.999.... The ellipses indicate that the 9's will repeat ad infinitum. This number is always smaller than 1, but . . .

lim[n → ∞] (10n - 1)/10n = 1

The above identity says that the limit of the expression equals 1; it doesn't say that in some moment, as n approaches infinity, 0.999... suddenly becomes identical to integer 1. But in practical applications, such as in calculus, various limits are treated as an exact representation of the results that involve numbers that are approaching certain values through a convergence, but never reach them. The margin of error is simply "infinitely small", and can be safely neglected. No one ever went wrong by doing so.

There are surely kids out there who now believe that 0.999... as a number where the 9s repeat infinitely doesn't simply exist and that Doron has been right after all saying that a straight line has "blind spots" -- that there are segments on that line that cannot be covered by points.

OM does not agree with the notion that a given existing space is completely covered by any given previous existing space, and it does not matter if the considered spaces are strict or non-strict.

Such a notion is strictly developed beyond the notion of Limit, and it is based on the difference between Locality and Non-locality, which can't be comprehended by the reasoning that defines Limits.

The reasoning of Limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Even if we ignore the place value system, the notion of distinct 0() spaces along 1() unconditionally leads to the conclusion that there are distinct 0() spaces along 1() only if there is ≠ between them, and ≠ is clearly free of any 0() space, otherwise no two arbitrary distinct 0() spaces along 1() can be defined.

jsfisher

22nd October 2010, 07:14 PM

http://en.wikipedia.org/wiki/0.999...#Skepticism_in_education

Just sayin'

You, sir or madam, are trivializing Doron's breath and depth of cognitive limitations.

epix

22nd October 2010, 10:10 PM

The reasoning of Limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Doron, it's "limits" not "Limits," therefore a limit cannot join the OM gods that you named Fullness and Emptiness and engage in some lewd act of reasoning. Change the letter case and you find out that limits don't have a mind to comprehend anything -- the folks who use them do.

The limits are essential in calculus. Without them, there would be no calculus and without calculus we would be on the same scientific level when there was no calculus.

You used inequality 3.1415... < Pi. How do you know what the decimal digits of Pi look like? Did you go through the result of the "traditional math" and simply copied them? Why don't you let Fulness and Emptiness get closer to the exact value of Pi, which will always remain unknown?

You think that there is no difference between rational and irrational numbers as far as the approximate value is concerned, and that the approximate value of Pi is getting more precise through 3, 3.1, 3.14, 3.141 and so on, but it doesn't go like that. The ever-more precise approximate form is a result of various summation formulas, and Pi is the limit when the number of summands is approaching infinity. One of the summation formula is the simple looking one that Euler came up with, and it goes like this:

pi = √[6*(1/12 + 1/22 + 1/32 + 1/42 + ...)]

It is said to approach Pi very slow, so I became curious how slow and found out that a dead snail is faster. It takes about ten million additions to get the first seven digits right!

http://img697.imageshack.us/img697/210/eulersum.png

The very first value is √6, which is 2.449....

So I wonder if Fullness and Emptiness can churn out a formula that outruns the one Euler came up with. Organic Mathematics shouldn't rely on the obsolete traditional approach; it should come up with its own version to account for the approximate rendition of number Pi, right?

doronshadmi

23rd October 2010, 02:17 AM

Organic Mathematics shouldn't rely on the obsolete traditional approach; it should come up with its own version to account for the approximate rendition of number Pi, right?

You are still missing the fact that according OM, no given space ( whether it is strict ( like 0.999() or PI() ),
or non-strict ( like 0.999…[base 10]() or 3.14...[base 10]() ) ) is defined by other spaces.

All you have to do is to get the difference between (just for example) non-complex spaces like:

∞[B](
0(),0.999…(),1(),2(),3(), PI()…
[B])

and complex results like:

∞(
... PI(3(2(1(0.999…(0()))))) ...
[B])

Traditional Math can't comprehend that "≠" is the non-local property of 1() w.r.t 0().

Furthermore, Traditional Math actually claims that 1() is completely covered by 0() , which is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0.

--------------

Again,

OM does not agree with the notion that a given existing space is completely covered by any given previous existing space, and it does not matter if the considered spaces are strict ( for example: PI() ) or non-strict ( for example: 3.14...() ).

Such a notion is strictly developed beyond the notion of Limit, and it is based on the difference between Locality and Non-locality, which can't be comprehended by the reasoning that defines Limits.

The reasoning of limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Even if we ignore the place value system, the notion of distinct 0() spaces along 1() unconditionally leads to the conclusion that there are distinct 0() spaces along 1() only if there is ≠ between them, and ≠ is clearly free of any 0() space, otherwise no two arbitrary distinct 0() spaces along 1() can be defined.

The limits are essential in calculus. Without them, there would be no calculus and without calculus we would be on the same scientific level when there was no calculus.

What is called traditional calculus, is simply a system that uses techniques which avoid non-strict results.

It does not mean that there can't be an extension of that system, which also deals with non-strict results, such that (for example)
[B]1 - 0.999… = [B]0.000…1[base 10]

doronshadmi

23rd October 2010, 09:47 AM

By the way, OM is different than the notion of Infinitesimals ( http://en.wikipedia.org/wiki/Infinitesimal ) or the notion of Non-standard analysis ( http://en.wikipedia.org/wiki/Non-standard_analysis ) which uses Infinitesimals, because the Infinitesimals are still taken as strict numbers , such that there is a strict number h that is smaller than all positive 1/n, and 1/h > any positive R member.

The Man

23rd October 2010, 11:07 AM

Some reading problems?

Just yours, as usual.

The considered number is smaller than any arbitrary number of (0,1] AND it is also > 0.

In other words, this considered number is not 1 AND it is not 0.

Again the interval (0,1] doesn’t restrict a member of the resulting set from being 1 while the interval (0,1) does.

doronshadmi

23rd October 2010, 01:48 PM

Again the interval (0,1] doesn’t restrict a member of the resulting set from being 1 while the interval (0,1) does.
Unless it is clearly written that the considered member is smaller than any arbitrary number of (0,1], where 1 is one of these arbitrary numbers, and you simply can't get it.

epix

23rd October 2010, 03:27 PM

doronshadmi

23rd October 2010, 04:27 PM

The greatest and defining difference between Organic Mathematics and contemporary mathematics is that the former is purely intuitive and the latter is purely analytic.

Look, for example, at Relative Set Theory http://maths.york.ac.uk/www/sites/default/files/Hrbacek-slides.pdf .

This approach uses also different levels of existence, but it still misses the fact that a given level can't completely be defined by some previous level, because it does not understand Emptiness (that has no predecessor) and Fullness (that has no successor).

Any given existing thing between these totalities has predecessor AND successor, such that there are strict ( for example: PI() ) or non-strict ( for example: 3.14…() ) things that appear as non-complex ( for example: ∞[b]( PI() , 3.14…() [b]) ) or complex ( for example: ∞( PI(3.14…()) [b]) ) forms.

OM is the linkage between Intuition and Analysis, where Traditional Math is mostly Analysis.

The Man

23rd October 2010, 04:58 PM

Unless it is clearly written that the considered member is smaller than any arbitrary number of (0,1], where 1 is one of these arbitrary numbers, and you simply can't get it.

Doron, your nonsense assertions don’t help you, Please let us know when you actually find your “considered member” that is “smaller than any arbitrary number” of the interval. Much like your location on a line that can not be covered by points once you identify a location you show that it is and can be covered by a point. In fact your own assertions indicate that a location must be a point. Once you indentify your “considered member” you’ll also indentify an infinite number of members of that interval that it is larger than.

epix

23rd October 2010, 05:43 PM

What is called traditional calculus, is simply a system that uses techniques which avoid non-strict results.

Calculus doesn't avoid handling values that approach zero -- it just handles them properly. You are under a wrong impression that in

a = [lim n → ∞] (1 + 1/n)n

the term 1/n gets simply canceled, coz it's "infinitely small" with the result being

a = [lim n → ∞] (1 + 1/n)n = (1 + 1/n)n = 1n = 1

Such "avoidance" is not possible, coz you have a number that approaches infinity in the exponent and that means the infinitely small value added to 1 creates a sum that will infinitely multiply itself. That's why you just can't cancel anything that appears to be "too small," and therefore your are heading in this particular case for a solution of

a = (1 + 1/n) ∙ (1 + 1/n) ∙ (1 + 1/n) ∙ (1 + 1/n) ∙ ...

You just jump into any conclusion, for you know that Fullness and Emptiness shall lift you up in their hands, so that you shall not strike your foot against a stone. (It's not just "Philosophy"; its "Religion & Philosophy".)

Feed it to OM and let's see what kind of result that method of yours comes up with. Or is it true that calculus handles problems, which OM doesn't have the slightest idea that they could exist?

epix

23rd October 2010, 06:50 PM

Look, for example, at Relative Set Theory http://maths.york.ac.uk/www/sites/default/files/Hrbacek-slides.pdf .

This approach uses also different levels of existence, but it still misses the fact that a given level can't completely be defined by some previous level, because it does not understand Emptiness (that has no predecessor) and Fullness (that has no successor).

The alleged shortcomings don't seem to have any impact on the ability to find the derivative of a function, for example. Why don't you identify a particular problem that only OM can deal with? "Emptiness" and "Fullness" never appear other than names -- they can't be spotted in the graph, in algebraic terms, equations... They only contribute to the solution of

(O - - M - - -) = (O l y M p u s)

doronshadmi

23rd October 2010, 11:15 PM

In fact your own assertions indicate that a location must be a point.

I see that your 0()-only reasoning prevents from you to get http://forums.randi.org/showpost.php?p=6472238&postcount=12096.

doronshadmi

23rd October 2010, 11:43 PM

Why don't you identify a particular problem that only OM can deal with?

I see that your conservative view of "What is the mathematical science?" prevents from you to grasp OM's novel approach about Logic\Ethics linkage, and its connection the Complexity in evolutionary scale, as expressed by:

http://www.scribd.com/doc/16547236/EEM

http://www.scribd.com/doc/16669828/EtikaE

You also ignore OM's novel contribution to Zeno's Achilles\Tortoise Race:

http://www.scribd.com/doc/21967511/Zeno-s-Achilles-Tortoise-Race-and-Reconsiderations-of-Some-Mathematical-Paradigms.

You also ignore OM's Non-locality\Locality novel approach:

http://www.scribd.com/doc/18453171/International-Journal-of-Pure-and-Applied-Mathematics-Volume-49

You are aslo ignore OM's novel contribution for the understanding of the common source of both Intuition and Analysis:

http://www.scribd.com/doc/17039028/OMDP

You also ignore OM's novel contribution to Hilbert's 6th problem:

http://www.scribd.com/doc/16542245/OMPT

In other words epix, you simply have no case.

zooterkin

24th October 2010, 04:31 AM

I see that your 0()-only reasoning prevents from you to get http://forums.randi.org/showpost.php?p=6472238&postcount=12096.

No.

doronshadmi

24th October 2010, 05:11 AM

No.
Yes.

doronshadmi

24th October 2010, 05:15 AM

The alleged shortcomings don't seem to have any impact on the ability to find the derivative of a function, for example. Why don't you identify a particular problem that only OM can deal with? "Emptiness" and "Fullness" never appear other than names -- they can't be spotted in the graph, in algebraic terms, equations... They only contribute to the solution of

(O - - M - - -) = (O l y M p u s)
Why do you ignore the rest of http://forums.randi.org/showpost.php?p=6474140&postcount=12101 ?

jsfisher

24th October 2010, 08:48 AM

the greatest and defining difference between organic mathematics and contemporary mathematics is that the former is purely counter-intuitive and the latter is purely analytic.

fify.

epix

24th October 2010, 10:55 AM

Any given existing thing between these totalities has predecessor AND successor, such that there are strict ( for example: PI() ) or non-strict ( for example: 3.14…[base 10]() ) things that appear as non-complex ( for example: ∞( PI() , 3.14…() [b]) ) or complex ( for example: ∞( PI(3.14…()) [b]) ) forms.

You should elaborate further to highlight the difference between the complex and non-complex case.

non-complex: ∞( PI() , 3.14…() [b])

complex: ∞( PI(3.14…()) [b])

The only discernible difference is the placement of the parenthesis and that's not enough to decode the essence between both opposites non-complex and complex besides the non-complex is to together() as complex is to apart( ).

You decided on using the parenthesis as a part of your symbolic syntax, but you use them often as delimiters in the text, and so that makes is it harder to follow. They say that Serpent had no successor, but I strongly disagree . . .

The Man

24th October 2010, 11:04 AM

I see that your 0()-only reasoning prevents from you to get http://forums.randi.org/showpost.php?p=6472238&postcount=12096.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

I see you still have not answered this question…

Location a long 1() is exactly 0().

"≠" still isn't a location.

Are you claiming that any location “a long 1() is exactly” a point?

Nor have you identified any location(s) on a line that is not and can not be covered by points.

doronshadmi

25th October 2010, 01:38 AM

The only discernible difference is the placement of the parenthesis
No, it is about (nested AND complex forms) OR (non-nested AND non-complex forms), where the considered things are strict ( for example: PI() ) or non-strict ( for example: 3.14...[base 10]() ).

According OM, 3.14...[base 10](PI()) is false expression, where PI(3.14...[base 10]()) is true expression.

doronshadmi

25th October 2010, 01:45 AM

Are you claiming that any location “a long 1() is exactly” a point?
Yes, any given exact location along 1() is 0().

Nor have you identified any location(s) on a line that is not and can not be covered by points.
Still your 0()-only reasoning can comprehend http://forums.randi.org/showpost.php?p=6472238&postcount=12096.

You are a total 0()-loss and there is no use to continue the dialog with you on this interesting subject.

zooterkin

25th October 2010, 02:45 AM

Yes, any given exact location along 1() is 0().

Right, so there is no location on the line where there is not a point?

doronshadmi

25th October 2010, 03:44 AM

fify.

Traditional Math actually claims that 1-dim space is completely covered by 0-dim elements , which is equivalent to the claim that variable x ( where x is any arbitrary distinct 0-dim element of [0,1] ) is both ≤ 1 OR both ≥ 0.

So sell your counter-intuitive fantasy in never never land.

doronshadmi

25th October 2010, 03:46 AM

Right, so there is no location on the line where there is not a point?
There is no exact location on a line where there is no point, and ≠ is such non-exact location on a line, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points).

epix

25th October 2010, 03:53 AM

No, it is about (nested AND complex forms) OR (non-nested AND non-complex forms), where the considered things are strict ( for example: PI() ) or non-strict ( for example: 3.14...[base 10]() ).

According OM, 3.14...[base 10](PI()) is false expression, where PI(3.14...[base 10]()) is true expression.

So if I'm not sure, I can use the identity 1pi(radian) = 180(degree) to avoid the aproximate form pi = 3.14..., right?

doronshadmi

25th October 2010, 03:57 AM

So if I'm not sure, I can use the identity 1pi(radian) = 180(degree) to avoid the aproximate form pi = 3.14..., right?

If you get http://forums.randi.org/showpost.php?p=6470162&postcount=12091 you allready know the answer.

epix

25th October 2010, 04:17 AM

There is no exact location on a line where there is no point, and ≠ is such non-exact location on a line, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points).
That's not true. The function f(x) = (x2 - 4)/(x - 2) is not defined for x = 2, so you can't see the point drawn at that exact location.

http://img138.imageshack.us/img138/5445/missingpoint1.png

The OM seems to be a very different computational method. Some drawings would be helpful . . .

zooterkin

25th October 2010, 04:21 AM

doronshadmi

25th October 2010, 05:44 AM

Back to the gibberish, I see.
Never gives up of ignorance, I see.

doronshadmi

25th October 2010, 05:59 AM

That's not true. The function f(x) = (x2 - 4)/(x - 2) is not defined for x = 2, so you can't see the point drawn at that exact location.

http://img138.imageshack.us/img138/5445/missingpoint1.png

The OM seems to be a very different computational method. Some drawings would be helpful . . .
Epix, you can use any function that you wish.

It does not change the fact that there is ≠, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points) that are the strict results of the given function.

≠ is definitely free of any strict results, which gives it the ability to be used both as differentiator AND integrator of the concept of Pair.

Without, for example, 1(0(x)≠0(y)) there is no pair.

epix

25th October 2010, 01:27 PM

Epix, you can use any function that you wish.

It does not change the fact that there is ≠, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points) that are the strict results of the given function.

Who says that it isn't so? Any xi that is a part of R is distinct, such as xi-1 < xi < xi+1. That's why you can see a line. You claim that point [x = 2, y = 4] doesn't have an exact location. Did you hack the Hubble telescope and see something not round "at the end" of 2.000... and 4.000...?

Eventually, there has to be point p > 2 that you express as p = 2.000...1. That means the "strict" number 2 is not immortal. Or is it?

You are applying your everyday experience into an abstract world that is not physical, and that creates a conflict. But that's normal:

a4 = a * a * a * a

a3 = a * a * a

a2 = a * a

a1 = a

a0 = ?

a0 seems to be the same case as a/0.

12/4 = 12 - 3 - 3 - 3

12/3 = 12 - 4 - 4

12/2 = 12 - 6

12/1 = 12

12/0 = ?

Both analogies are not identical, as far as the result is concerned, even though your intuition tells you that they are.

doronshadmi

26th October 2010, 01:24 AM

You claim that point [x = 2, y = 4] doesn't have an exact location.
Wrong, 1(0(2)≠0(4)) is 1() (notated by ≠) between strict numbers.

Eventually, there has to be point p > 2 that you express as p = 2.000...1. That means the "strict" number 2 is not immortal. Or is it?
2.000...1() is a non strict number (where the concept of Number is a measurement tool, whether the measured is a strict or non-strict level of existence or a given strict or non-strict location), for example:

0(2) is a valid expression, 0(2.000...1) is an invalid expression, 2.000...1(0(2)) is a valid expression.

Again, the general form is X(x), where X is strict or non-strict level of existence, and x is strict or non-strict location, such that X=0 has only strict locations (also X=0 does not have sub-levels of existence), and X>0 has (strict OR non-strict locations) OR (strict OR non-strict sub-levels of existence).

You are applying your everyday experience into an abstract world that is not physical, and that creates a conflict. But that's normal:

a4 = a * a * a * a

a3 = a * a * a

a2 = a * a

a1 = a

a0 = ?

a0 seems to be the same case as a/0.

12/4 = 12 - 3 - 3 - 3

12/3 = 12 - 4 - 4

12/2 = 12 - 6

12/1 = 12

12/0 = ?

Both analogies are not identical, as far as the result is concerned, even though your intuition tells you that they are.

No, 0 < a0 = 1 < a/0 = ∞ < ∞

epix

26th October 2010, 12:26 PM

Epix, you can use any function that you wish.

It does not change the fact that there is ≠, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points) that are the strict results of the given function.

Arbitrary points are not "the strict results of the given function," as they cannot be given their definition. The result of a given function is not an arbitrary point -- that point is defined by the function. An arbitrary point is the independent variable, and the value of the dependent variable... well, depends on the way the independent variable is treated by the function f(x). In other words, f(x) = y, where x is the independent, or arbitrary, variable and y is the dependent variable. So, for x = 2, the function

f(x) = (x2 - 4)/(x - 2) = 0/0

and the corresponding dependent variable y doesn't exist on the y-axis, coz the function doesn't define it (division by zero). That means there can't be no point drawn on the line that visualizes the f(x) = y relationship. Remember that integer 2 and real number 2 are not the same: in the latter case, 2 is a short for 2.000.... Unlike in a = 2.333... where a is approaching limit 7/3, the integers of real numbers are not approaching any limit and are therefore exact numbers.

2.33333 - 2.333 > 0

but

2.00000 - 2.000 = 0

That's why there is one and only one point missing in the straight line that represents the function f(x) above and that's why algebra uses fractional representation of non-integer numbers, which is the limit.

Since OM doesn't recognize the function as an instrument that graphically displays values of the modified independent variable, there is no way to prove that assertions made by OM are true or false.

The Man

26th October 2010, 01:54 PM

Yes, any given exact location along 1() is 0().

So then there are no locations on your line that are not or can not be covered by points as you assert “any given exact location” is a point.

Still your 0()-only reasoning can comprehend http://forums.randi.org/showpost.php?p=6472238&postcount=12096.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

You are a total 0()-loss and there is no use to continue the dialog with you on this interesting subject.

You can stop any time. Or can you?

There is no exact location on a line where there is no point, and ≠ is such non-exact location on a line, which exists between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points).

“≠” still isn’t a location Doron and you simply inserting “exact” and “non-exact into your dichotomist terminology doesn’t change that.

Please identify any location “between any given arbitrary pair of distinct exact locations (arbitrary pair of distinct points)” that is not or can not be covered by points.

doronshadmi

26th October 2010, 10:39 PM

So then there are no locations on your line that are not or can not be covered by points as you assert “any given exact location” is a point.

Again,

Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0() ( as expressed by 1(0(x)≠0(y)) ), or simply the fact that 1() is at AND beyond 0() ( as expressed by 1(0()) ).

≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0(y)) Pair.

Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.

The Man, your 0()-only reasoning is too weak in order to deal with 1(0()) or 1(0(x)≠0(y)).

You can write as many replies as you wish, which does not change the fact that you are closed under 0()-only reasoning, which is weaker than 1(0()) reasoning.

zooterkin

26th October 2010, 10:44 PM

Again,

Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0(), which expressed as 1(0(x)≠0(y)).

≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0(y)) Pair.

Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.

So, you still can't identify a location on a line where there is no point? Got it. Do you think you could stop claiming that you can?

doronshadmi

26th October 2010, 11:20 PM

Arbitrary points are not "the strict results of the given function," as they cannot be given their definition. The result of a given function is not an arbitrary point -- that point is defined by the function. An arbitrary point is the independent variable, and the value of the dependent variable... well, depends on the way the independent variable is treated by the function f(x). In other words, f(x) = y, where x is the independent, or arbitrary, variable and y is the dependent variable. So, for x = 2, the function

f(x) = (x2 - 4)/(x - 2) = 0/0

and the corresponding dependent variable y doesn't exist on the y-axis, coz the function doesn't define it (division by zero). That means there can't be no point drawn on the line that visualizes the f(x) = y relationship. Remember that integer 2 and real number 2 are not the same: in the latter case, 2 is a short for 2.000.... Unlike in a = 2.333... where a is approaching limit 7/3, the integers of real numbers are not approaching any limit and are therefore exact numbers.

2.33333 - 2.333 > 0

but

2.00000 - 2.000 = 0

That's why there is one and only one point missing in the straight line that represents the function f(x) above and that's why algebra uses fractional representation of non-integer numbers, which is the limit.

Since OM doesn't recognize the function as an instrument that graphically displays values of the modified independent variable, there is no way to prove that assertions made by OM are true or false.

You are simply still missing the fact that f(x) is equivalent to 1(0()), such that f() is equivalent to 1() and x (if it is strict) is equivalent to 0().

Remember that integer 2 and real number 2 are not the same:
Wrong, 2 or 2.000... is exactly the same 0().

You are still missing 2.000...1(0(2)), such that 2.000...1() - 0(2) = 0.000...1(), which can be expressed as 2.000...1(0.000...1())

doronshadmi

26th October 2010, 11:23 PM

So, you still can't identify a location on a line where there is no point? Got it. Do you think you could stop claiming that you can?
So, you can't comprehend 1(0()) or 1(0(x)≠0(y))! Got it.

Do you think you could stop claiming that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction?

epix

27th October 2010, 12:35 AM

You are simply still missing the fact that f(x) is equivalent to 1(0()), such that f() is equivalent to 1() and x (if it is strict) is equivalent to 0().
This is the reason why OM cannot display its own version of a f(x) graph, coz the definitions, based on the OM terminology, are the insurmountable obstacle. The traditional math understands that f() doesn't make sense without the indication which independent variables are to be modified by the function, and so f() never appears in the text, except in the case of non-mathematical applications where f() may substitute the traditional f... as a brief comment that summarizes certain unexpected outcomes.

In OM, f() = 1() means that a function without independent variables equals a one-dimensional space (:confused:). You decided to notate a one-dimensional space as 1(), coz you didn't worry about a possible conflict with f(x), coz you never use it. Following the meaning of 1(), it's inevitable that f() implies an f-dimensional space and not a function where the independent variable(s) are not present.

I think you need to come up with correcting syntax ideas and edit all the posts that you have written.

epix

27th October 2010, 01:03 AM

Wrong, 2 or 2.000... is exactly the same 0().

I didn't refer to the value of 2 and 2.000... Just read again.

epix

27th October 2010, 01:38 AM

Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.

Your conclusion is contradictory by itself and the reason is that you can't still grasp the meaning and the usage of intervals despite all the explaining links provided.

Suppose that an insurance analyst wants to know the probability that a person dies due to a specific illness between the age of 65 and 75 including, where the age of the person upon expiring is defined as X. He collects sample data, does some number crunching and finds out that the probability P is

P(65 ≤ X ≤ 75) = .68 [68%]

That person who gets unlucky doesn't die twice at the age of 65 and 75; it dies only once in the age that is within the range indicated. That person dies only once, coz he or she lives only once. Just don't get confused by some high-powered theoretical claims based on the latest research in genetics done by Prof. Sinatra. (http://www.youtube.com/watch?v=XgFtQPgHyek)

doronshadmi

27th October 2010, 03:18 AM

In OM, f() = 1() means that a function without independent variables equals a one-dimensional space (:confused:).
In OM X() is a level of strict of non-strict existence, which exists independently of any sub-levels. X can be number, function, dimensional space, or any measurable strict or non-strict level of existence.

I think you need to come up with correcting syntax ideas and edit all the posts that you have written
You still do not get the generalization of X(), such that a given X's existence is independent of any other given X.

doronshadmi

27th October 2010, 04:16 AM

Your conclusion is contradictory by itself and the reason is that you can't still grasp the meaning and the usage of intervals despite all the explaining links provided.
epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0(y) value.

In other words, no given level of existence is completely covered by any collection of previous levels of existence, whether the previous levels are non-strict ( like 0.999...[base 10]() ) or strict ( like 0(x) ).

You are still missing, for example: 1(0.999...[base 10]()), 1(0(x)≠0(y)), 0.999...[base 10](0(x)), etc ...

epix

27th October 2010, 11:49 AM

In OM X() is a level of strict of non-strict existence, which exists independently of any sub-levels. X can be number, function, dimensional space, or any measurable strict or non-strict level of existence.

Can you provide an example of some function that you notate "f()" -- function with a certain level of strictness, as it exists non-strictly?

Where does the level of strictness appear in the term X()? Is it inside the parenthesis, or is it outside? Does f(2) mean that the function f() has the second level of strictness? You never mentioned that there are certain levels of strictness.

Just provide an example of two functions of the second and the third level of strict existence, so the difference could be seen. Follow the example of the traditional function: For x = 5

f(x) = 2x + 3 = 2*5 + 3 = 13

epix

27th October 2010, 12:13 PM

epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0(y) value.

No one has ever argued anything like that. You are still confused by the meaning of the term explained here:
http://forums.randi.org/showpost.php?p=6485624&postcount=12134

Once again . . .
Let x be a positive integer. Then

65 ≤ x ≤ 75 means that x can take on values from 65 to 75.

65 < x < 75 means that x can take on values from 66 to 74.

65 < x ≤ 75 means that x can take on values from 66 to 75.

65 ≤ x < 75 means that x can take on values from 65 to 74.

The Man

28th October 2010, 08:19 AM

Again,

Traditional Math can't comprehend that ≠ is the non-local property of 1() w.r.t 0(), such that ≠ is the existence of 1() between any given arbitrary pair of distinct 0() ( as expressed by 1(0(x)≠0(y)) ), or simply the fact that 1() is at AND beyond 0() ( as expressed by 1(0()) ).

Doron if you are trying to claim that two points define a line segment, well, that is exactly what “Traditional Math” and the geometry claims.

Once again your assertion that “1() is at AND beyond 0()” simply shows that you can’t even agree with yourself.

≠ is definitely free of any 0(), which gives it the ability to be used both as differentiator AND integrator of the concept of 1(0(x)≠0(y)) Pair.

Once again Doron, “≠“ is simply an assertion of inequality. However, in a continuous space there is always at least another point between any two points.

Again please identify any location(s) on a line segment that is not and can not be covered by points.

Moreover, Traditional Math's claim that 1() is completely covered by 0() is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction.

No Doron your continued misrepresentation of the symbols “≤ “ “≥” only makes your claim “equivalent” to your own misrepresentation.

To try to clarify it again for you, any point included in the interval [0,1] is > 0 AND < 1, OR = 1, OR = 0. Your “both ≤ 1 OR both ≥ 0” claim is just nonsense and only shows that you do not understand the “≤” and “≥” symbols. “Both” < OR = (“both ≤ “) as well as “both” > OR = (“both ≥”) is a contradiction and it remains simply yours.

The Man, your 0()-only reasoning is too weak in order to deal with 1(0()) or 1(0(x)≠0(y)).

You can write as many replies as you wish, which does not change the fact that you are closed under 0()-only reasoning, which is weaker than 1(0()) reasoning.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

The Man

28th October 2010, 08:25 AM

Do you think you could stop claiming that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction?

Do you think you can actually learn what the symbols “≤” and “≥” represent, evidently you simply do not want to.

As you're the only one making that ridiculous and nonsensical claim Doron, only you can stop making it and stop trying to attribute it to others. Or can you?

epix

28th October 2010, 03:44 PM

epix, you can't grasp that strict 0(x) value can't be = AND ≠ to strict 0(y) value.

In other words, no given level of existence is completely covered by any collection of previous levels of existence.
Well, I really can't grasp it, but you should stick with the ethics and not mention certain taboos. There are social taboos, but there are also academic taboos. The traditional math is inconsistent and one of the cases that demonstrates it is the one that you keep complaining about and the essence of that case is that the traditional math asserts A = B and at the same time A ≠ B. More specifically, it is the case of identity and difference that you complain about and should not. Any ethical mathematician looks the other way, but you are an OM mathematician not fond of the traditional math, so that explains the breach of the taboo.

You didn't mention a particular case of the contradiction that may be responsible for so many problems unsolved -- problems that the best mathematicians have been trying to crack, but to no avail. Perhaps if I describe a particular case of the inconsistency based on that horrendous contradiction, you may find some solution to the predicament -- if I'm that naive.

Suppose that a person wants to travel from point A to point B.

A_________________B

But that individual cannot control all the circumstances connected with the intended activity. (http://www.youtube.com/watch?v=osocGiofdvc) Obviously, the following case (1) cannot equal at the same time case (2).

1) A____________B
2) A______ ____B

But the traditional math asserts that it can.

Definition: A line is not continuous if at least one point on it is not defined by the function that creates such a line.

Here is an example of such a discontinuity; it is function

f(x) = (x2 - 4)/(x - 2)

http://img138.imageshack.us/img138/5445/missingpoint1.png

This function is not defined for x = 2, coz the function returns result 0/0 and that's why the blue straight line is not continuous at point x = 2.

The applied consequence is that you cannot finish your intended trip -- the bridge is gone. But the traditional math asserts that you can.

http://img255.imageshack.us/img255/4033/missingpoint2.png

You see that there is a function

g(x) = x + 2

that entirely covers the blue line drawn by f(x) and therefore

f(x) = g(x)

But the identity suffers from a contradiction; namely, the point x = 2 that is not defined for f(x) is defined for g(x):

f(x=2) = (22 - 4)/(2 - 2) = 0/0 [division by zero]
g(x=2) = 2 + 2 = 4

Here is the contradiction in more formal view:

If f(x) = g(x) then f(x=2) = g(x=2) and therefore 'not defined' = '4'

Facing such a catastrophe, it is commanding to make sure that f(x) really equals g(x) using algebra. Since

x2 - 4 = (x - 2) ∙ (x + 2)

it follows that

f(x) = (x2 - 4)/(x - 2) = [(x - 2) ∙ (x + 2)]/(x - 2) = [(x - 2) ∙ (x + 2)]/(x - 2) = x + 2 = g(x)

and the contradiction holds.

This contradiction is a result of a much broader logical inconsistency that regards quantum/analog reasoning, and it appears in the results many a scientific field come up with. For example in

1) Simian DNA______ _______Human DNA
2) Simian DNA______________Human DNA

The evolution of human species is a theory that is allowed to exist despite the presence of various "missing links," coz

If f(x) = g(x) then (1) = (2).

You've been feverishly working for two years to collapse the world of ours, Doron, but Jesus is our Savior, and He will make sure that we will continue to live in mental darkness, happily ever after the way Adam and Eve were supposed to and free of uncertainties the source of which we cannot fix. Surely, some bridges will collapse, some planes will crash due to the f(x) = g(x) design, but we can make other attributes and continue to believe in academic Santa Klaus.

doronshadmi

29th October 2010, 06:15 AM

Can you provide an example of some function that you notate "f()" -- function with a certain level of strictness, as it exists non-strictly?

Where does the level of strictness appear in the term X()? Is it inside the parenthesis, or is it outside? Does f(2) mean that the function f() has the second level of strictness? You never mentioned that there are certain levels of strictness.

Just provide an example of two functions of the second and the third level of strict existence, so the difference could be seen. Follow the example of the traditional function: For x = 5

f(x) = 2x + 3 = 2*5 + 3 = 13

Again, X (in terms of existence) thet is expressed as X(), can be strict ( for example PI() ), or non-strict ( for example 3.14…() ).

The relations between non-strict 3.14…[base 10]() and strict PI() can be non-complex ( for example: ∞[B]( PI() , 3.14…() [B]) ) or complex ( for example: ∞( PI(3.14…()) [B]) ).

In the case of complexity OM uses X(x) form, where X or x can be strict, or non-strict.

For example: according to OM, 3.14...[base 10](PI()) is X(x) false expression, where PI(3.14...[base 10]()) is true X(x) expression.

Does f(2) mean that the function f() has the second level of strictness?

No. f(2) is based on X(x) that is the general form of Complexity, where X(x) (such that X can be strict or non-strict) has sub-level x (such that x can be strict or non-strict).

By following the notion of non-complexity, X() exists independently of x, such that ∞( X() , x ), where your given particular case is ∞( f() , 2 ).

Does f(2) mean that the function f() has the second level of strictness?
No, it simply means that:

1) We are using X(x), which is the general form of complexity.

2) Your chosen particular expression under (1) is the strict function f(x) = 2x + 3 = 13

doronshadmi

29th October 2010, 06:41 AM

Do you think you can actually learn what the symbols “≤” and “≥” represent, evidently you simply do not want to.

As you're the only one making that ridiculous and nonsensical claim Doron, only you can stop making it and stop trying to attribute it to others. Or can you?
Your 0()-only reasoning simply can't get that the claim that "1-dim space is completely covered by 0-dim spaces" is equivalent to the claim that (for example) "variable x ( where x is any arbitrary distinct member of [0,1] ) is both ≤ 1 OR both ≥ 0".

Both claims are definitely a contradiction.

doronshadmi

29th October 2010, 06:48 AM

However, in a continuous space there is always at least another point between any two points.

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1 is equivalent to ≠ between [B]0.999... and [B]1, if we avoid mixed bases.

doronshadmi

29th October 2010, 07:02 AM

Definition: A line is not continuous if at least one point on it is not defined by the function that creates such a line.
Wrong. 1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence.

OM expresses this notion as 1(0()).

doronshadmi

29th October 2010, 07:15 AM

No one has ever argued anything like that. You are still confused by the meaning of the term explained here:
http://forums.randi.org/showpost.php?p=6485624&postcount=12134

Once again . . .
Let x be a positive integer. Then

65 ≤ x ≤ 75 means that x can take on values from 65 to 75.

65 < x < 75 means that x can take on values from 66 to 74.

65 < x ≤ 75 means that x can take on values from 66 to 75.

65 ≤ x < 75 means that x can take on values from 65 to 74.
Whether it is N or R collection of x elements (where any arbitrary x is 0-dim space) , it does no change the fact that there is always ≠ between any given pair of 0-dim spaces along 1-dim space, which prevents form any amount of 0-dim spaces to completely cover 1-dim space.

epix, you have missed http://forums.randi.org/showpost.php?p=6474902&postcount=12106 .

zooterkin

29th October 2010, 08:01 AM

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1 is equivalent to ≠ between [B]0.999... and [B]1, if we avoid mixed bases.

More nonsense. There is no such thing as the ...1, and even if there were, it would not be equivalent to a ≠ sign.

psionl0

29th October 2010, 08:58 AM

This debate has so far gone on for 304 pages??

G.I.G.O.

The Man

29th October 2010, 09:59 AM

It can't help you to avoid ≠ between some arbitrary distinct pair.

Who is trying to “avoid ≠ between some arbitrary distinct pair”? Again the fact that the points are not equal means in a continuous space that there is always at least a third point not equal to either of those two between them.

For example: the ...1 of 0.000...1 is equivalent to ≠ between [B]0.999... and [B]1, if we avoid mixed bases.

No Doron, as you have been told before your “ ...1” following “0.000...” is just meaningless as “0.000...” represents an infinite series of zeros after the decimal place.

Now if you are trying to claim some non-zero infinitesimal difference between 1 and 0.9999..., then your “points” are no longer zero dimensional, having that non-zero infinitesimal extent.

Wrong. 1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence.

OM expresses this notion as 1(0()).

Really? So if the points A and B were equal would your “1-dim space” exist between those points? It is in fact you who are trying “to avoid ≠ between some arbitrary distinct pair” and the dependence of the “1-dim space” on and resulting from that inequality.

Doron, to try to put it more succinctly for you, if “1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence” then the “0-dim space” is simply not a “sub-level of” that “1-dim space”. Again if you want that non-zero difference between 1 and 0.999... Then your “sub-level” (your “point“) is simply not a “0-dim space”.

The Man

29th October 2010, 10:01 AM

This debate has so far gone on for 304 pages??

G.I.G.O.

Indeed, and still evidently just around in circles.

Welcome to the forum and thread psionl0.

epix

29th October 2010, 01:00 PM

For example: the ...1 of 0.000...1 is equivalent to ≠ between [B]0.999... and [B]1, if we avoid mixed bases.

How can 0.000...1 be rendered in number base 1, when the number is made of 2 different digits (zeroes and one)?

See, after your couple of replies that again demonstrate your math illiteracy, I'm not sure if that "base 1" is a typo or not.

epix

29th October 2010, 01:29 PM

It can't help you to avoid ≠ between some arbitrary distinct pair.

For example: the ...1 of 0.000...1 is equivalent to ≠ between [B]0.999... and [B]1, if we avoid mixed bases.

Your notation doesn't allow to visualize both numbers as they approach their limits, as the standard math can. You can't also find the exact point of intersection.

http://img132.imageshack.us/img132/7407/graph1b.png

Also, your notation cannot prove that "0.999..." added to "0.000...1" equals 1, as f(x) + g(x) can, coz your notation lacks algebraic terms necessary for the proof.

You need to re-write everything into the standard math language and edit all your posts.

doronshadmi

29th October 2010, 01:43 PM

Doron if you are trying to claim that two points define a line segment, well, that is exactly what “Traditional Math” and the geometry claims.
“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

1(0(x) ≠ 0(y)) is a general expression of the concept of Segment, such that any given arbitrary segment 0(x) ≠ 0(y) is ( non-extendible to 1() ) AND ( irreducible to 0() ).

Once again your assertion that “1() is at AND beyond 0()” simply shows that you can’t even agree with yourself.

Once again your reasoning, where “1() is defined by 0()” simply shows that you can’t comprehend 1() as independent of any sub-spaces.

As e result you have no ability to comprehend 1(0(x)), where 1() is at AND beyond 0(x).

doronshadmi

29th October 2010, 01:47 PM

See, after your couple of replies that again demonstrate your math illiteracy, I'm not sure if that "base 1" is a typo or not.

The Man, it is a typo, and your poor maneuvers around it simply demonstrate your no-motivation to understand OM.

zooterkin

29th October 2010, 02:18 PM

The Man, it is a typo, and your poor maneuvers around it simply demonstrate your no-motivation to understand OM.

I think you'll find you are replying to epix, not The Man.

zooterkin

29th October 2010, 02:21 PM

“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

Ah, yes, Traditional Math(s), which has given us things such as space travel, computers and many other things we see around us today.

Now, remind me what you can do with OM. Have you yet produced a single example of what use it is? Or even a simple, understandable, example of an expression in it?

epix

29th October 2010, 03:39 PM

I think you'll find you are replying to epix, not The Man.
Under OM, 1()epix is = AND 1()The Man, and so epix=The Man. Your 0()-only reasoning doesn't allow you to grasp a simple concept.

;)

epix

29th October 2010, 05:26 PM

Ah, yes, Traditional Math(s), which has given us things such as space travel, computers and many other things we see around us today.

Now, remind me what you can do with OM.
OM application mainly concerns the time travel. Once are the mathematicians able to grasp that "1() that is 1-dimensional space with no sub-dimensional spaces along it," we are right back in the 15th century.

The Man

30th October 2010, 01:29 AM

“Traditional Math”, which is the reasoning that you are using all along this thread, can't comprehend 1() that is 1-dimensional space with no sub-dimensional spaces along it.

Wrong again Doron, your simply lack of self-consistency and general consistency does not infer that any one lacks comprehension other than you.

1(0(x) ≠ 0(y)) is a general expression of the concept of Segment, such that any given arbitrary segment 0(x) ≠ 0(y) is ( non-extendible to 1() ) AND ( irreducible to 0() ).

“non-extendible to 1()”? So now your “concept of Segment” isn’t even one dimensional?

Once again your reasoning, where “1() is defined by 0()” simply shows that you can’t comprehend 1() as independent of any sub-spaces.

Well it is not surprising that you simply do not comprehend the meaning of a “sub-space“.

As e result you have no ability to comprehend 1(0(x)), where 1() is at AND beyond 0(x).

Once again Doron your obvious and evidently deliberate lack of self-consistency is entirely comprehensible to everyone but you.

doronshadmi

30th October 2010, 11:50 AM

Also, your notation cannot prove that "0.999..." added to "0.000...1" equals 1, as f(x) + g(x) can, coz your notation lacks algebraic terms necessary for the proof.

Wrong.

0.999...+[B]0.000...1=[B]1 has the necessary algebraic terms.

On the contrary the Limit concept does not have the necessary algebraic terms, because it can't explain how a given distinct 0-dimesional space x reaches distinct 0-dimensioanl space y , such that ( there is nothing between 0(x) and 0(y) ) AND ( 0(x) ≠ 0(y) ).

doronshadmi

30th October 2010, 11:53 AM

I think you'll find you are replying to epix, not The Man.

Thank you zooterkin.

Sorry The Man, my mistake.

doronshadmi

30th October 2010, 12:06 PM

OM application mainly concerns the time travel. Once are the mathematicians able to grasp that "1() that is 1-dimensional space with no sub-dimensional spaces along it," we are right back in the 15th century.

Wrong epix,

We will enter to the 21 century with the ability to distinguish between the Local and the Non-local, and the ability to distinguish between the complex and the non-complex.

A better understanding of Complexity is essential for the survival of complex phenomenon like us in the vary near and far future, and OM is one of the possible ways to develop the awareness of the importance of Complexity's better understanding.

It can't be done if the place value is taken as system of numerals, which prevents any understanding of the existence of non-local numbers, which are essential to our measurement and better understanding of Complexity.

epix, you systematically continue to ignore http://forums.randi.org/showpost.php?p=6474902&postcount=12106, I wonder why :rolleyes:

“non-extendible to 1()”? So now your “concept of Segment” isn’t even one dimensional?
Here is a concrete example of the devastating influence of "Traditional Math" on The Man's reasoning, which prevents from him to understand the difference between 1(), 1(0(x)≠0(y)) and 0().

epix

30th October 2010, 01:17 PM

Wrong.

0.999...+[B]0.000...1=[B]1 has the necessary algebraic terms.
Where are they? There is no woman that would believe BD claims until she sees it.

On the contrary the Limit concept does not have the necessary algebraic terms, because it can't explain how a given distinct 0-dimesional space x reaches distinct 0-dimensioanl space y , such that ( there is nothing between 0(x) and 0(y) ) AND ( 0(x) ≠ 0(y) ).
The concept of the limit got nothing to do with your gross misinterpretation. Point 'x' moves along the horizontal axis and point 'y' moves along the vertical axis with only one possible point of intersection and that's point [0,0] -- the origin. So there can't be x - y = 0 and at the same time x - y ≠ 0 as your day-dreaming claims. Your interpretation of how standard math should work and doesn't is affected by your symbolic illiteracy of it. That's why you didn't comment on the contradiction here
http://forums.randi.org/showpost.php?p=6492023&postcount=12141
coz you don't have the slightest idea what's going on in there.

doronshadmi

31st October 2010, 12:29 AM

Where are they? There is no woman that would believe BD claims until she sees it.
http://forums.randi.org/showpost.php?p=6453327&postcount=12048 is in front of your mind, but your wrong notions about the considered subject simply prevent from you to get it, all along this thread.

That's why you didn't comment on the contradiction here
http://forums.randi.org/showpost.php?p=6492023&postcount=12141
coz you don't have the slightest idea what's going on in there.
Wrong epix, all you have is to look at http://forums.randi.org/showpost.php?p=6494154&postcount=12145.

The concept of the limit got nothing to do with your gross misinterpretation. Point 'x' moves along the horizontal axis and point 'y' moves along the vertical axis with only one possible point of intersection and that's point [0,0] -- the origin. So there can't be x - y = 0 and at the same time x - y ≠ 0 as your day-dreaming claims. Your interpretation of how standard math should work and doesn't is affected by your symbolic illiteracy of it.

You are not with me epix.

0(x) and 0(y) are points along 1-dimensional space like the real-line, for example, where by OM the real-line is 1-dimensional space ( notated by 1() ), which exists independently of any existing sub-space along it, where 0() is such a sub-space.

As for your 2-dimensional space ( notated by 2() ) it exits independently of any sub-spaces like 1() or 0().

Also you are using wrong notions like

"Point 'x' moves along the horizontal axis and point 'y' moves along the vertical axis
epix, you have to enter the following fundamental fact to your mind:

No sub-space moves along a given space. All we have is strict or non-strice sub-spaces w.r.t a given (strict or non-strict ) space, for example:

0.999...[base 10] is a non-strict sub-space w.r.t 1() strict space, and 0() is a strict sub-space w.r.t 1() strict space.

Your claim that 0(x) or 0(y) moves along 1() clearly demonstrates that you can't comprehend 0() as totally local AND strict space that essentially can't move form its strict location.

doronshadmi

31st October 2010, 05:24 AM

Really? So if the points A and B were equal would your “1-dim space” exist between those points?
No, because actually there exists only one 0(), no matter how many names it has.

It is in fact you who are trying “to avoid ≠ between some arbitrary distinct pair” and the dependence of the “1-dim space” on and resulting from that inequality.
1) If A and B are distinct from each other, you can’t avoid ≠ between them, so your claim is false.

2) The existence of 1() is independent of any existing sub-space along it.

Doron, to try to put it more succinctly for you, if “1-dim space exists independently of any sub-levels of existence along it, where 0-dim space is such sub-level of existence” then the “0-dim space” is simply not a “sub-level of” that “1-dim space”.
The Man, the existence of 1() is independent of 0(), whether 0() exists or does not exist as 0() along it.

Your limited 0()-only reasoning can’t comprehend the independence of spaces w.r.t each other, whether they are defined as non-complex ( 1(), 0() ) or complex ( 1(0()) ) forms.

Now if you are trying to claim some non-zero infinitesimal difference between 1 and 0.9999..., then your “points” are no longer zero dimensional, having that non-zero infinitesimal extent.
Wrong.

For example: Local number 0.000... (a point, which is 0-dim space) < Non-local number 0.000...1[base 10], where ...1 is a line (a 1-dim space) between Non-local number 0.999...[base 10] (a complex of 1 and 0 dim spaces) and Local number 1 (a point, which is 0-dim space).

doronshadmi

31st October 2010, 06:02 AM

Well it is not surprising that you simply do not comprehend the meaning of a “sub-space“.
Wrong.

Let us take, for example 3() and 2():

You can’t comprehend that 3() exists independently of any 2() spaces w.r.t it, as clearly seen in the following diagram:
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Secretsharing-3-point.png/220px-Secretsharing-3-point.png
http://en.wikipedia.org/wiki/Euclidean_subspace

It has to be stressed that this diagram is a piece of 3() space, which has a form of a cube, where a cube is a complex w.r.t 3() exactly as a line segment is a complex w.r.t 1().

The Man

31st October 2010, 10:38 AM

No, because actually there exists only one 0(), no matter how many names it has.

So the existence of your “1-dim space” does depend on the existence of more than one point. I’m glad that you have finally come to realize that.

1) If A and B are distinct from each other, you can’t avoid ≠ between them, so your claim is false.

I claimed you were trying not that you were succeeding. Your next assertion shows clearly that you are still “trying “to avoid ≠ between some arbitrary distinct pair” and the dependence of the “1-dim space” on and resulting from that inequality” and still not succeeding

2) The existence of 1() is independent of any existing sub-space along it.

You have just asserted above that it is dependent on the existence of more than one point.

The Man, the existence of 1() is independent of 0(), whether 0() exists or does not exist as 0() along it.

Again see your first assertion quoted above where you claim the “existence of” your “1()” is dependent on there being more than one point.

Your limited 0()-only reasoning can’t comprehend the independence of spaces w.r.t each other, whether they are defined as non-complex ( 1(), 0() ) or complex ( 1(0()) ) forms.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Evidently you simply can not comprehend the meaning of the word independence.

Wrong.

For example: Local number 0.000... (a point, which is 0-dim space) < Non-local number 0.000...1[base 10], where ...1 is a line (a 1-dim space) between Non-local number 0.999...[base 10] (a complex of 1 and 0 dim spaces) and Local number 1 (a point, which is 0-dim space).

So after I state the consequences of a non-zero infinitesimal, you then say “Wrong.” and proceed to assert that you are in fact using a non-zero infinitesimal and evidently would simply prefer to ignore those consequences. So how many points are “between Non-local number 0.999...[base 10] (a complex of 1 and 0 dim spaces) and Local number 1 (a point, which is 0-dim space)”?

Wrong.

Let us take, for example 3() and 2():

You can’t comprehend that 3() exists independently of any 2() spaces w.r.t it, as clearly seen in the following diagram:
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Secretsharing-3-point.png/220px-Secretsharing-3-point.png
http://en.wikipedia.org/wiki/Euclidean_subspace

It has to be stressed that this diagram is a piece of 3() space, which has a form of a cube, where a cube is a complex w.r.t 3() exactly as a line segment is a complex w.r.t 1().

Next time try actually reading the article instead of just looking at the pictures.

Definition
A Euclidean subspace is a subset S of Rn with the following properties:
1. The zero vector 0 is an element of S.
2. If u and v are elements of S, then u + v is an element of S.
3. If v is an element of S and c is a scalar, then cv is an element of S.
There are several common variations on these requirements, all of which are logically equivalent to the list above.[4] [5]

The Man

31st October 2010, 10:46 AM

Thank you zooterkin.

Sorry The Man, my mistake.

No problem, you accidently attributing a quote from epix to me is of little concern. However, you deliberately trying to attribute your own assertions to others, well, when are you going to apologize for that?

ETA:

For example….

Do you think you could stop claiming that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0, which is definitely a contradiction?

Do you think you can actually learn what the symbols “≤” and “≥” represent, evidently you simply do not want to.

As you're the only one making that ridiculous and nonsensical claim Doron, only you can stop making it and stop trying to attribute it to others. Or can you?

Your 0()-only reasoning simply can't get that the claim that "1-dim space is completely covered by 0-dim spaces" is equivalent to the claim that (for example) "variable x ( where x is any arbitrary distinct member of [0,1] ) is both ≤ 1 OR both ≥ 0".

Both claims are definitely a contradiction.

Again just you unapologetically trying to pawn off your own (evidently deliberate) ignorance and assertions on to others

epix

31st October 2010, 02:08 PM

http://forums.randi.org/showpost.php?p=6453327&postcount=12048 is in front of your mind, but your wrong notions about the considered subject simply prevent from you to get it, all along this thread.

What you demonstrate got nothing to do with algebraic terms. I've already replied to that argument of yours, but you simply disregarded it, coz your argument went up the smoke.

Here is a related example of a complete backwardness of OM: There are two finite positive numbers a and b such as a < 1 and b < 1. Number a has twenty thousand zeroes after the decimal point and ends with 1318; number b has twenty-five thousand zeroes after the decimal point and ends with 666. How does OM express the multiplication of both numbers and its result; how does a*b = c look like in OM?

epix

31st October 2010, 02:27 PM

Your 0()-only reasoning simply can't get that the claim that "1-dim space is completely covered by 0-dim spaces" is equivalent to the claim that (for example) "variable x ( where x is any arbitrary distinct member of [0,1] ) is both ≤ 1 OR both ≥ 0".

You always mention the word "equivalent" but never write down the actual equation that would demonstrate the argument in the language standard math speaks with. If you have anything against standard math, you need to show where it stutters. Your OM translation of the alleged problem is illegal; such a translation is maybe permissible in translating the Bible, but math is not a religion. You need to demonstrate that your mind isn't the one of a fanatic priest but a mind of a mathematician.

epix

31st October 2010, 03:21 PM

The Man

31st October 2010, 04:16 PM

Originally Posted by doronshadmi
Your 0()-only reasoning simply can't get that the claim that "1-dim space is completely covered by 0-dim spaces" is equivalent to the claim that (for example) "variable x ( where x is any arbitrary distinct member of [0,1] ) is both ≤ 1 OR both ≥ 0".

Both claims are definitely a contradiction.

According to OM, plural=singular.

That really seems to be his problem of late epix. That for some reason he seems to think some point must be both greater than and equal to zero as opposed to just one point being equal to zero and all other points (in the interval) being greater than zero. I think it really comes back to his non-zero infinitesimal assertions, where such a non-zero infinitesimal would encompass both zero and greater than zero to some infinitesimal but non-zero extent. It is rather bizarre though that he asserts “any arbitrary distinct member of [0,1]” as opposed to just two specific ones. Since in the interval (0,1) all members are greater than zero and less then one. While for the interval [0,1] zero and one are now also members of that interval. So the only difference is the inclusion of the two boundary points in the closed interval that are not included in the open. Thus the majority of a collection of “arbitrary distinct member of [0,1]” would be both greater than zero and less than one, while only one specific “distinct member of [0,1]” equals zero and only one specific “distinct member of [0,1]” equals one. Further he claims “both ≤ 1 OR both ≥0” (so it is "both" one "OR" "both" the other) as if he has simply divided the interval into two subsets and “any arbitrary distinct member of [0,1]” must encompass one subset or the other and both subsets must include one boundary point each.

epix

31st October 2010, 10:38 PM

Further he claims “both ≤ 1 OR both ≥0” (so it is "both" one "OR" "both" the other) as if he has simply divided the interval into two subsets and “any arbitrary distinct member of [0,1]” must encompass one subset or the other and both subsets must include one boundary point each.
If you conceive a total logical goulash, then you won't be able to serve it in the bowl shaped by the standard math expressive symbolism, and that's what is happening to Doron. Just follow the yellow line . . .
The same goes for his "equivalencies" that he can express only verbally, such as "your claim is equivalent to . . . ," but he never writes down the equation to show you where you go allegedly wrong. Instead, he goes into a verbal assertive mode supplemented by OM notation made of parenthesis and numbers. The more he feels that he messed up, the more parenthesis appear in his defensive arguments. In that case, he also adds more afterthoughts and explanatory remarks enclosed in ( ), so it all makes a lovely configuration reminiscent of Salvator Dali paintings.

doronshadmi

1st November 2010, 04:23 AM

So the existence of your “1-dim space” does depend on the existence of more than one point.
No The Man.

1-dim space exists independently of any sub-space like 0-dim space along it.

Your 0-only reasoning simply can't get anything without using 0-dim space.

So how many points are “between Non-local number 0.999...[base 10] (a complex of 1 and 0 dim spaces) and Local number 1 (a point, which is 0-dim space)”?
If only non-local number 0.999... and local number [B]1 are considered, then there is 0.000...1 between them , such that [B]...1 is a line (with no points along it) between 0.999... and [B]1.

doronshadmi

1st November 2010, 04:41 AM

No problem, you accidently attributing a quote from epix to me is of little concern. However, you deliberately trying to attribute your own assertions to others, well, when are you going to apologize for that?

ETA:

For example….

Again just you unapologetically trying to pawn off your own (evidently deliberate) ignorance and assertions on to others

Your limited 0-only reasoning is exactly the framework that its users\developers have to apologize in front of the the people around the world, because they are deliberately forcing their ignorance for the past 3000 years on our civilization and block any improvement of the understanding of Complexity and its essential building-blocks.

Next time try actually reading the article instead of just looking at the pictures.
Next time try to understand that your 0-only reasoning can't comprehend the independence of the existence of spaces w.r.t each other.

Definition
---------------
A Euclidean subspace is a subset...http://en.wikipedia.org/wiki/Euclidean_subspace

No The Man, a space is not a collection, and you simply can't get it because your reasoning is limited to 0-only elements.

doronshadmi

1st November 2010, 04:52 AM

What you demonstrate got nothing to do with algebraic terms. I've already replied to that argument of yours, but you simply disregarded it, coz your argument went up the smoke.

Here is a related example of a complete backwardness of OM: There are two finite positive numbers a and b such as a < 1 and b < 1. Number a has twenty thousand zeroes after the decimal point and ends with 1318; number b has twenty-five thousand zeroes after the decimal point and ends with 666. How does OM express the multiplication of both numbers and its result; how does a*b = c look like in OM?

So now your smoke prevents from you to get what have been written in http://forums.randi.org/showpost.php?p=6499689&postcount=12164.

doronshadmi

1st November 2010, 05:03 AM

zooterkin

1st November 2010, 05:07 AM

doronshadmi

1st November 2010, 05:12 AM

If you conceive a total logical goulash,

The logical goulash is done by you, when you claim that:

"Point 'x' moves along the horizontal axis and point 'y' moves along the vertical axis

Do you understand that a point is totally local where immobility is one of its essentials?

doronshadmi

1st November 2010, 05:16 AM

0.000...1[base 10] exists only in your imagination, as does a line with no points on it.
It is better than your imagination, which according to it totally local and different distinct 0-dim spaces completely cover a 1-dim space.

doronshadmi

1st November 2010, 05:47 AM

oppsss..

sympathic

1st November 2010, 08:09 AM

It is better than your imagination, which according to it totally local and different distinct 0-dim spaces completely cover a 1-dim space.

Of course it is. Doron's imagination by far excels over everyone else's. In fact he should probably change "OM" to "IM" for "Imaginary Math".

epix

1st November 2010, 01:36 PM

Wrong.

Let us take, for example 3() and 2():

You can’t comprehend that 3() exists independently of any 2() spaces w.r.t it, as clearly seen in the following diagram:
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Secretsharing-3-point.png/220px-Secretsharing-3-point.png
http://en.wikipedia.org/wiki/Euclidean_subspace

It has to be stressed that this diagram is a piece of 3() space, which has a form of a cube, where a cube is a complex w.r.t 3() exactly as a line segment is a complex w.r.t 1().
It must be so "clear" that the writer who contributed to the unrelated topic in Wiki didn't bother to support your assertion. The truth of the matter is though that the writer didn't get infected by OM, and so the concurrence is missing from the text. Obviously, you don't have the slightest idea what the text is all about, otherwise you wouldn't use it as a supporting argument for one of your declaration of independence.

The shape of a 3-dim object depends on

f(x,y) = z

where x and y are the independent variables and z, which makes the 3rd dimension, is the dependent variable. Since we live in 3-dim space, you can crumple a sheet of paper. The way the crumpled sheet looks like depends exactly on f(x,y) = z. How do you think I made this "stool?"

http://img339.imageshack.us/img339/5306/seat1h.jpg

Note that the shape is enclosed in a cube. Does it ring a bell? Do you know what happens when you stack up 2-dim spaces?
http://www.mytechinterviews.com/wp-content/uploads/2010/06/ryanlerch_deck_of_cards.png

The manipulation of a matrix can be considered a 2-dim algebra, and so there can be a natural extension:
http://en.wikiversity.org/wiki/Investigating_3D_geometric_algebra

There is something that 3-dim algebra and OM have in common:

Unfortunately Geometric algebra is often introduced using many terms and symbols that are foreign to most people, the result being that it remains inaccessible to many without a sufficient background in Mathematics.

There is also a profound difference and we all know what it is: Clifford knew what he was doing.

epix

1st November 2010, 06:11 PM

So now your smoke prevents from you to get what have been written in http://forums.randi.org/showpost.php?p=6499689&postcount=12164.
Your reference is a poor excuse bag staffed with irrelevancy and it can't avert the disaster OM is heading for, e.g. it is becoming obvious that OM cannot manipulate very small but finite numbers, coz it doesn't have the means to express them.

Here it is once again:

There are two finite positive numbers a and b such as a < 1 and b < 1. Number a has twenty thousand zeroes after the decimal point and ends with 1318; number b has twenty-five thousand zeroes after the decimal point and ends with 666. How does OM express the multiplication of both numbers and its result; how does a*b = c look like in OM?

You better start inventing, if you want that 'M' in the acronym stand for "Mathematics," and not for "Miscarriage" (of reason).

epix

1st November 2010, 09:43 PM

Do you understand that a point is totally local where immobility is one of its essentials?
If you had used other letters than x and y, which are letters reserved for points that lie on the x and y coordinates, I wouldn't have to be that descriptive. You put anything that you call 1() object into one bag and make far-reaching conclusions . . .

Btw, the description of a point "moving" isn't something that would wreak havoc with some math ideas put forward:
"Conversely, if a point moves continuously on the sphere, then the ray through it also rotates continuously, and therefore the point X at which the ray..." (http://books.google.com/books?id=R9vPatr5aqYC&pg=PA57&lpg=PA57&dq=point+x+moves&source=bl&ots=c7mOr66jja&sig=PhNQG6cPqcl0bK8bQpHL_9EqG0A&hl=en&ei=24_PTJXyB4aqsAOt7NSgAw&sa=X&oi=book_result&ct=result&resnum=9&ved=0CDgQ6AEwCA#v=onepage&q=point%20x%20moves&f=false)

So, there is no reason to GET EXCITED,

x = ?

x = the thief, he kindly spoke.

????? ??????x (http://www.youtube.com/watch?v=9WbKBKima4Q)

doronshadmi

1st November 2010, 10:56 PM

epix, all of your last posts have a common failure.

They can't comprehend the independence of different things w.r.t each other, such that no thing is defined by any other thing, accept itself.

As a result you can't distinguish between the non-complexity of , for example 3() (3-dim space) and 0(x,y) or 0(x,y,z) w.r.t to 3(), where 3() holds even if there are no 0(x,y) or 0(x,y,z) w.r.t to it.

This notion is true for any given thing, whether it is strict (like PI()) or non-strict ( like 3.14...(PI()) is an example of false expression, and PI(3.14...[base 10()) is an example of true expression, even if 3.14...[base 10] and PI() are independent w.r.t each other under the given complex false and true examples.

By understanding the independent of Emptiness (that has no predecessor) and Fullness (that has no successor) w.r.t each other, one immediately understands that any thing between some predecessor and some successor, is independent of any given predecessor or any given successor exactly as Emptiness is defined independently of any successor and Fullness is defined independently of any predecessor.

So even if we are dealing with several things and get a complex, this complex does not change the fact that any thing of that complex is independent of the other things that share this complex.

For example, your notion of a line segment can't comprehend the following notions:

1) No line segment, which is at most 1(0(x)≠0(y)) w.r.t 1(), is 1().

2) No line segment, which is at least 1(0(x)≠0(y)) w.r.t 0(), is 0().

A diagram of (1) and (2) facts is:

..._____________________.__________.______________ ____________________ ...

where 1(), which is represented by ..._______________..., is at AND beyond any given 0(), which is represented by . along 1().

By understanding (1) and (2), it is immediately understood that .__________. is non-extendible to ..._______________... AND irreducible to .

It must be so "clear" that the writer who contributed to the unrelated topic in Wiki didn't bother to support your assertion.
You are right epix, because he\she and you suffering of the same misunderstanding that does not comprehend the independence of different things w.r.t each other.

Let us take again the example of 3() and 2():

You can’t comprehend that 3() exists independently of any 2() spaces w.r.t it, as clearly seen in the following diagram:
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Secretsharing-3-point.png/220px-Secretsharing-3-point.png
http://en.wikipedia.org/wiki/Euclidean_subspace

Moreover, each given 2() in this diagram is independent of any other 2().

You have missed this important part:

[B]It has to be stressed that this diagram is a piece of 3() space, which has a form of a cube, where a cube is a complex w.r.t 3() exactly as a line segment is a complex w.r.t 1(), as can be seen by the following diagram:

..._____________________.__________.______________ ____________________ ...

Btw, the description of a point "moving" ...

"moving" ≠ moving

doronshadmi

2nd November 2010, 01:02 AM

Of course it is. Doron's imagination by far excels over everyone else's.

sympathic it simply avoids the contradiction that is derived from the imagination which claims that distinct and different 0-dim spaces completely cover 1-dim space.

The claim that 0-dim spaces completely cover 1-dim space is equivalent to the claim that
an arbitrary pair of different and distinct 0-space are = AND ≠ w.r.t each other.

epix

2nd November 2010, 12:14 PM

You can’t comprehend that 3() exists independently of any 2() spaces w.r.t it, as clearly seen in the following diagram:
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Secretsharing-3-point.png/220px-Secretsharing-3-point.png
http://en.wikipedia.org/wiki/Euclidean_subspace

Let's consider a cube with axis U, S and A that has volume 1776 units. Independence is rendered with those 2-dim spaces OUTSIDE the cube, NOT INSIDE. as you demonstrate, coz the modification of a 2-dim subspace affects the property of a 3-dim space, coz both differently dimensioned spaces share the same coordinates 'x' and 'y'. Independence is about apart and not together. You need to quote from any related text so the quote would directly address the issue of independency between an n-dim object and its subspace.

You shouldn't worry about that anyway, coz you still need to demonstrate that OM is capable of multiplying very small but finite numbers.

epix

2nd November 2010, 01:28 PM

Do you understand that a point is totally local where immobility is one of its essentials?

there was once a local point
that decided to smoke a joint
as its lungs got really busy
the point became really dizzy

with no value, with no sign
it fell quickly off the line
that's what happened, now you prove
that the point just couldn't move. (http://www.safetysignsupplies.co.uk/images/product_imgs/full/965_2_3.gif)

doronshadmi

3rd November 2010, 03:11 AM

coz the modification of a 2-dim subspace affects the property of a 3-dim space

Wrong, any given space is essentially independent of any other space.

You are talking about the dependency under the complex results among independent spaces.

Let me give you an example:

The existence of 1-dim and 0-dim spaces are independent of each other, such that if one of them is missing, the other one still exists.

Now let's observe a complex like line-segment, which is the result of the linkage among 1() and 0().

Even if the length of 1() space under the complex, called line-segment, depends on the values of 0() spaces, it does not mean the 1() or 0() existence depend on each other.

doronshadmi

3rd November 2010, 03:22 AM

You shouldn't worry about that anyway, coz you still need to demonstrate that OM is capable of multiplying very small but finite numbers.
0.000...1[base 10], for example, is not a finite number, but it is the irreducibility of 1() to 0() upon infinitely many scales.

doronshadmi

3rd November 2010, 04:56 AM

there was once a local point
that decided to smoke a joint
as its lungs got really busy
the point became really dizzy

with no value, with no sign
it fell quickly off the line
that's what happened, now you prove
that the point just couldn't move. (http://www.safetysignsupplies.co.uk/images/product_imgs/full/965_2_3.gif)

Yet "moving" ≠ moving.

The Man

3rd November 2010, 10:25 AM

No The Man.

1-dim space exists independently of any sub-space like 0-dim space along it.

Doron a space is not independent of its sub-space. Though you have made it quite clear that you simply do not understand the meaning of the word independent or the concept of sub-spaces.

Your 0-only reasoning simply can't get anything without using 0-dim space.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

If only non-local number 0.999... and local number [B]1 are considered, then there is 0.000...1 between them , such that [B]...1 is a line (with no points along it) between 0.999... and [B]1.

So your non-zero infinitesimal is your “point” and your “point” is not zero dimensional having that non-zero infinitesimal extent, as asserted before.

Your limited 0-only reasoning is exactly the framework that its users\developers have to apologize in front of the the people around the world, because they are deliberately forcing their ignorance for the past 3000 years on our civilization and block any improvement of the understanding of Complexity and its essential building-blocks.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

OK so “improvement” is evidently another word you simply do not understand.

Next time try to understand that your 0-only reasoning can't comprehend the independence of the existence of spaces w.r.t each other.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Again a space is not independent of its sub-spaces nor are those sub-spaces independent of that space.

http://en.wikipedia.org/wiki/Euclidean_subspace

No The Man, a space is not a collection, and you simply can't get it because your reasoning is limited to 0-only elements.

Again try actually reading the article. As explained to you before the sub-spaces of a line segment can be represented as line segments. This “limited to 0-only elements” fantasy of yours is, well, just yours and you simply want to continue unapologetically trying to ascribe it to others.

The Man, you still do not get that your R members are exactly distinct 0() spaces, and each distinct 0() space is different from another distinct 0() space only if there is 1() space between them, where only 1() can be at AND beyond the location of any given distinct 0() (which is a property that no 0() space has.)

Which once again makes your “1()” dependent on there being more than one “distinct 0()”. That they depend upon each other ( your “1()” and your “another distinct 0()”) does not make them independent but mutually dependent.

It is better than your imagination, which according to it totally local and different distinct 0-dim spaces completely cover a 1-dim space.

Again identify any location or locations in a “a 1-dim space” that is not and can not be covered by a zero dimensional point or points.

They can't comprehend the independence of different things w.r.t each other, such that no thing is defined by any other thing, accept itself.

Doron you simply can not comprehend if “no thing is defined by any other thing, accept itself” then there is no definable relation to “any other thing”.

sympathic it simply avoids the contradiction that is derived from the imagination which claims that distinct and different 0-dim spaces completely cover 1-dim space.

The claim that 0-dim spaces completely cover 1-dim space is equivalent to the claim that
an arbitrary pair of different and distinct 0-space are = AND ≠ w.r.t each other.

Once again Doron the contradiction remains simply yours as “The claim that 0-dim spaces completely cover 1-dim space is” certainly not “equivalent to the claim that an arbitrary pair of different and distinct 0-space are = AND ≠ w.r.t each other”

Simply changing your “equivalent” claim to some other contradiction still does not make it equivalent to “The claim that 0-dim spaces completely cover 1-dim space” or any less simply your own deliberately contradictory claim that you simply want to try to ascribe it to others.

epix

3rd November 2010, 01:34 PM

Originally Posted by epix
You shouldn't worry about that anyway, coz you still need to demonstrate that OM is capable of multiplying very small but finite numbers.

0.000...1[base 10], for example, is not a finite number, but it is the irreducibility of 1() to 0() upon infinitely many scales.

Whom do you reply to?

epix

3rd November 2010, 02:44 PM

Wrong, any given space is essentially independent of any other space.

Of course there are cases where the independency holds. Suppose that the pic you've presented as a "proof"
http://en.wikipedia.org/wiki/File:Secretsharing-3-point.png
shows a plastic box with three sheets of cardboard paper as the 2-dim subspaces. You can rearrange the sheets any way you wish but that shuffling around wouldn't affect the size and the shape of the plastic box, the same way stirring goulash will not affect the size and shape of the cooking pot. This is an observation that may intrigue a one-year old baby, but can we like move along ahead on the timeline?

doronshadmi

3rd November 2010, 11:35 PM

Whom do you reply to?
To one called epix.

doronshadmi

3rd November 2010, 11:39 PM

Which once again makes your “1()” dependent on there being more than one “distinct 0()”. That they depend upon each other ( your “1()” and your “another distinct 0()”) does not make them independent but mutually dependent.

Your reply is wrong, as clearly shown in http://forums.randi.org/showpost.php?p=6510718&postcount=12190.

epix

3rd November 2010, 11:40 PM

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

And I bet that you don't type that. That's a copy/paste job START -> MY DOCUMENTS -> DORON_REPLIES.

:D

doronshadmi

3rd November 2010, 11:45 PM

Of course there are cases where the independency holds. Suppose that the pic you've presented as a "proof"
http://en.wikipedia.org/wiki/File:Secretsharing-3-point.png
shows a plastic box with three sheets of cardboard paper as the 2-dim subspaces. You can rearrange the sheets any way you wish but that shuffling around wouldn't affect the size and the shape of the plastic box, the same way stirring goulash will not affect the size and shape of the cooking pot. This is an observation that may intrigue a one-year old baby, but can we like move along ahead on the timeline?
epix, your transparent box is another collection of 2() spaces that there existence is independent of each other, and so is the 3() space that is used as their common environment, the 3() space exists whether it is used as a common environment of infinity many independent 2() spaces, or not.

If a timeline is what you call development, then in your case the time has 0() size.

epix

4th November 2010, 01:01 AM

If only non-local number 0.999... and local number [B]1 are considered, then there is 0.000...1 between them , such that [B]...1 is a line (with no points along it) between 0.999... and [B]1.

This is the problem OM has: that number that you express as 0.999... is not what you call a "local number." That number is approaching its limit 1, as the ellipses (...) indicate. The particular problem lies in the non-algebraic rendition of the number, which is "destined" to approach its limit "from the beginning":

0.9
0.99
0.999
0.9999
0.99999...

This number has its complementary value w.r.t. its limit that you can express only this way:

1 - 0.999... = 0.000...1

If you let p = 0.999... and q = 0.000...1, then also p = {0.9, 0.99, 0.999, 0.9999, 0.99999, ...}, coz p is a number whose value is approaching its limit -- number 1. Your weird intuition tells you that 0.9 is just too far away from 1 for p to be approaching its limit number 1. Since OM doesn't use functions, you can't convince yourself that p starts approaching its limit much sooner than you think it does. Since you claim that there is no point between q and 1, there can't be any point between 0.9 and 1 as well:

0___________________________0.9______1

In other words, there can't be point 0.95

0___________________________0.9__0.95__1

which divides the length of the line segment m = 1 - 0.9 = 0.1 in half.

You just couldn't comprehend the simple proof of you being wrong when it was rendered through a standard math language, coz you can't speak it nor can you read it. I bet that you won't again comprehend what was repeated to you by others, namely that the lenghth of a line segment no matter how short is represented by number a where a > 0, and any such number is divisible by any number b where b ≠ 0. The result of such a division appears as an additional point on a given line segment.

You claim that point p is an immediate predecessor of point z = 1, but elsewhere in the thread you agreed that there is no such a thing as immediate successor and predecessor. (Go and stir the goulash.)

Conclusion: There can't be a "line (with no points along it) between 0.999... and [B]1," unless the line segment is the phantasmagorical segment

O___________M

doronshadmi

4th November 2010, 01:16 AM

If you let p = 0.999... and q = 0.000...1, then also p = {0.9, 0.99, 0.999, 0.9999, 0.99999, ...}

Wrong, 0.999... is not a member of set {0.9, 0.99, 0.999, 0.9999, 0.99999, ...}

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1

sympathic

4th November 2010, 01:56 AM

It is amazing. This guy talks about infinity yet is unable to understand what it means. "0.0000....." means you repeat 0 infinite times, how can one put a "1" at the "end" of infinity?

epix

4th November 2010, 02:06 AM

Wrong, 0.999... is not a member of set {0.9, 0.99, 0.999, 0.9999, 0.99999, ...}

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1
:confused:
I thought that 0.999... rendered as a sum equals

0.999... = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + 0.000009 and so on without that 9 going after the bunch of 0's mysteriously changing to 1.

Well, in OM things happen different way . . .

So, Doron, what did you have for breakfast this morning? What? What clue? OM...?
Aaah, like hash browns?
No?
I was about to say that. (http://www.inhouserecipes.com/images/tomatoSpreadOmelet.jpg)

doronshadmi

4th November 2010, 02:23 AM

The Limit concept does not have the necessary algebraic terms, because it can't explain how a given distinct 0-dimesional space x reaches distinct 0-dimensioanl space y , such that ( there is nothing between 0(x) and 0(y) ) AND ( 0(x) ≠ 0(y) ).

Again,

Take a 1-dim element with finite size X.

Bend it and get 4 equal sides along it.

Since the size between the opposite edges is changed to the sum of only 3 sides, and since the number of the sides after the first bending is 4 sides, we have to multiply the bended 1-dim element by 1/(the number of the sides after some bending), in order to get back the finite constant size X > 0, etc ... ad infinitum ... , as shown in the diagram below.

As a result each bended 1-dim element has finite constant size X > 0, but the size between its opposite edges becomes smaller (it converges), and used to define S=2(a+b+c+d+...) .

In general, S size is unsatisfied because the bended 1-dim element has finite constant size X > 0 upon infinitely many bended levels of:

http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg

X is a constant length > 0.

Theorem: The length of X’s totally bended form ≠ The length of X’s totally non bended form.

1) Let us assume that constant X>0 is independent of the number of bends along it, by using the assumption that X is completely covered by 0-dimensioanl distinct spaces, whether it is bended or not.

2) According to (1) the length of X’s totally bended form = the length of X’s totally non bended form.

3) But the totally bended form is exactly a single 0-dimensional space and in this case X=0, which contradicts (2).

4) According to (3) we can conclude that The length of X’s totally bended form ≠ The length of X’s totally non bended form.

Q.E.D

doronshadmi

4th November 2010, 03:15 AM

0.999... = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + 0.000009 and so on without that 9 going after the bunch of 0's mysteriously changing to 1.

mysteriously? what mysteriously? what are you talking about?

0.999...[base 10] = 0.9[base 10] + 0.09[base 10] + 0.009[base 10] + ... < 1 by 0.000...1[base 10]

zooterkin

4th November 2010, 03:33 AM

doronshadmi

4th November 2010, 05:31 AM

Not to mention that once you have bent your '1-dim' element, it's not 1-dimensional any more.
Not according to Traditional Math, which claims that 1-dim is completely covered by 0-dims.

epix

4th November 2010, 01:05 PM

The Limit concept does not have the necessary algebraic terms, because it can't explain how a given distinct 0-dimesional space x reaches distinct 0-dimensioanl space y , such that ( there is nothing between 0(x) and 0(y) ) AND ( 0(x) ≠ 0(y) ).

That's because the concept of limits doesn't concern itself with "x reaching y"; it's the other way around.

Here is probably what you have a hard time to comprehend. Do you see any point between O and M?

O_____________________M

The line segment has only two defining points -- O and M -- so there is no other point between them. That's because you didn't chose it. Once you decide to do so, there is no way that you wouldn't be able to locate such a point.

Some functions are not defined for certain x, like f(x) = log 0, so there is no corresponding point y, but there is a corresponding point for any x > 0 and that includes a value that you notate as 0.000...1

Here are some y-values for f(x) = log(10) x

0.1 = -1
0.01 = -2
0.001 = -3
0.0001 = -4

You can see that as x approaches zero, y approaches negative infinity, or

[lim x → 0] log(10) x = -∞

x never reaches zero or any other limit number, coz that would collapse the concept of infinity: if the train stops, the name of the town is "Finity."

I very much doubt that the following link would change your mind, but I post it anyway.
http://ltcconline.net/greenl/courses/115/functionGraphLimit/limits.htm

epix

4th November 2010, 03:16 PM

mysteriously? what mysteriously? what are you talking about?

0.999...[base 10] = 0.9[base 10] + 0.09[base 10] + 0.009[base 10] + ... < 1 by 0.000...1[base 10]
The Summerian tablets are an exercise in eloquency when compared with this sorrowful scribble.

In your previous rendition, 0.000...1 was one of the addends

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1

and now it is not the part of the expansion and sits at the end of the whole expression separated from the expansion by < and preceded by by. Did you mean to invoke the situation where 0.000...1 is leaving saying bye-bye to the rest of the expression?

epix

4th November 2010, 04:05 PM

Theorem: The length of X’s totally bended form ≠ The length of X’s totally non bended form.

That's not a theorem due to the triviality of the proposition: (4X)/3 ≠ X.

doronshadmi

5th November 2010, 02:16 AM

Once you decide to do so, there is no way that you wouldn't be able to locate such a point.
Once you decide to do so, there is no way that you wouldn't be able to avoid a line between some arbitrary pair of points, where ...1 of the expression 0.000…1 is such a line.

x never reaches zero or any other limit number, coz that would collapse the concept of infinity: if the train stops, the name of the town is "Finity."
This is exactly OM's claim, which does not agree with Traditional Math, which claims that, for example 1/2+1/4+1/8+… = to limit 1.

Now we see that you simply wish to be against OM by principle, no matter if you agree or does not agree with what it claims.

doronshadmi

5th November 2010, 02:22 AM

The Summerian tablets are an exercise in eloquency when compared with this sorrowful scribble.

In your previous rendition, 0.000...1 was one of the addends

and now it is not the part of the expansion and sits at the end of the whole expression separated from the expansion by < and preceded by by. Did you mean to invoke the situation where 0.000...1 is leaving saying bye-bye to the rest of the expression?

Do you understand that 0.9, 0.09, 0.009., ... etc. are 0() spaces, where ...1 of 0.000...1 expression is 1() space ?

doronshadmi

5th November 2010, 02:37 AM

That's not a theorem due to the triviality of the proposition: (4X)/3 ≠ X.

Please look at

http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg

The length of X > 0 is invariant as long as the given element is not totally bended (where each bend is an 0-dimensional space).

Traditional Math claims that since 1-dimasional space is totally covered by 0-dimensional spaces, then constant X>0 is defined
even if 1-dimensioan space is totally bended.

OM shows the impossibility of such a claim, which is also related to the impossibility that, for example, 1/2+1/4+1/8+... = to limit 1.

epix

5th November 2010, 04:31 AM

Please look at

http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg

The length of X > 0 is invariant as long as the given element is not totally bended (where each bend is an 0-dimensional space).

Traditional Math claims that since 1-dimasional space is totally covered by 0-dimensional spaces, then constant X>0 is defined
even if 1-dimensioan space is totally bended.

Traditional math doesn't claim anything like that, coz the Koch curve is not a 1-dimensional space. Traditional math "claims" and can prove that the fractal dimension of Koch's curve is d = (log 4)/(log3).

Evidence of what traditional math claims and what it doesn't:
http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

doronshadmi

5th November 2010, 06:27 AM

Traditional math doesn't claim anything like that, coz the Koch curve is not a 1-dimensional space. Traditional math "claims" and can prove that the fractal dimension of Koch's curve is d = (log 4)/(log3).

Evidence of what traditional math claims and what it doesn't:
http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

It has infinite length.

http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

It seems that you are unaware of Traditional Math's claim about the equality of |R|, whether we deal with finite of infinite length.

This claim is based on the reasoning which claims that 1-dimensional space is totally covered by 0-dim spaces, and according to this reasoning, it does not matter if the considered form has infinitely of finitely bends along some considered length (finite or not) > 0.

In other words, you have no understanding of Traditional Math's claim about the equality of |R| of any arbitrary given length > 0, whether it is bended or not.

According to Traditional Math totally bended length X and totally not bended length X have cardinality |R|, but I prove in http://forums.randi.org/showpost.php?p=6514886&postcount=12204 that this is a false claim.

doronshadmi

5th November 2010, 06:56 AM

Traditional math "claims" and can prove that the fractal dimension of Koch's curve is d = (log 4)/(log3)
We are not talking here about fractal dimensions, but about the difference between totally bended and totally not bended (or not totally bended) forms.

Traditional Math simply can't understand that if the Koch's fractal (or any other arbitrary bended form) is totally bended, then its length = 0.

Instead, Traditional Math claims that a totally bended form (and Koch's fractal is just an example here) has an infinite length, and this mistake is clearly seen and written in http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html, which leads to the mistake that the number of points along a totally bended form, has cardinality (Cardinality in terms of Traditional Math) > 1.

In other words epix, your replies have nothing to do with my posts, on this subject.

doronshadmi

5th November 2010, 09:10 AM

In general, any converges or diverges value, which its size is defined upon infinitely many scale levels, is measured by non-strict numbers of the form 0.000…x, and it has a non-strict value, as can be seen by the following example of Koch's fractal:

http://upload.wikimedia.org/wikipedia/commons/8/89/Fractal_koch.png.
http://upload.wikimedia.org/wikipedia/commons/8/89/Fractal_koch.png

The Man

5th November 2010, 09:20 AM

Your reply is wrong, as clearly shown in http://forums.randi.org/showpost.php?p=6510718&postcount=12190.

No Doron you are simply and entirely wrong as usual. Once again a space is not independent of its sub-spaces.

doronshadmi

5th November 2010, 09:56 AM

No Doron you are simply and entirely wrong as usual. Once again a space is not independent of its sub-spaces.

The Man you have no case because you do not distinguish between the complex and the non-complex.

You are talking about the dependency under the complex results among independent spaces.

Let me give you an example:

The existence of 1-dim and 0-dim spaces are independent of each other, such that if one of them is missing, the other one still exists.

Now let's observe a complex like line-segment, which is the result of the linkage among 1() and 0().

Even if the length of 1() space under the complex, called line-segment, depends on the values of 0() spaces, it does not mean the 1() or 0() existence depend on each other.

epix

5th November 2010, 11:55 AM

This claim is based on the reasoning which claims that 1-dimensional space is totally covered by 0-dim spaces, and according to this reasoning, it does not matter if the considered form has infinitely of finitely bends along some considered length (finite or not) > 0.

I was right in my suspicion that you don't have the vaguest idea about the concept of points. If there is a location on 1-dim object, such as the initiator line of the Koch curve, that a point cannot define, then you can't "cut and bend" the line infinitely. That's because for that activity you need to locate the vertex and the inflection points. Any modification or a construction of objects with d>0 requires the presence of defining points, and you are totally oblivious to that fact. You only see that after one million iterations, the Koch curve still comprise combination of line segments and points and therefore there would be always a point-line-point segment, e.g. there would be always a space between two points "not covered by a point." But after another couple of million iterations you find that this particular line segment is littered with vertex points as the bending continues. Go back and look at the example once again. Do you see any other point apart from the endpoints?

O_____________________M

No?
The conclusion is then that this line segment is not entirely covered by points. That also means that this line segment can't become the generator of the Koch curve, coz you can't locate the necessary inflection and vertex points to modify the line. The reason why you can't locate the points is the absence of any points between O and M. That in turn means that the finite length of the O_M line cannot be divided by number 3, coz the result of such a division looks like

O_______|_______|_______M

and since there are no points between O and M, there is no way to define and locate the points through (M - O)/3. The general consequence is that Organic Mathematics discovered numbers greater than zero that are indivisible. (Applause.)

BUT! The concept of the limit says that there is always a space between two points on a curve, otherwise there would be no derivative of the function that draws such a curve, and without us being able to compute derivatives, the science time would stop in the 16th century. The length of such a pointless segment approaches zero -- zero is the limit. So in this respect, it's true that "line cannot be entirely covered by points." On the other hand, any line length can be further divided. That's a contradiction that the concept of infinity solves. You can locate any point on a curve and at the same time compute the derivative of the function that draws the curve. The result in the approximate format would be "infinitely precise," but not "exact."

PI is to EXACT as 3.1415... is to INFINITELY PRECISE

doronshadmi

5th November 2010, 03:24 PM

I was right in my suspicion that you don't have the vaguest idea about the concept of points. If there is a location on 1-dim object, such as the initiator line of the Koch curve, that a point cannot define, then you can't "cut and bend" the line infinitely. That's because for that activity you need to locate the vertex and the inflection points. Any modification or a construction of objects with d>0 requires the presence of defining points, and you are totally oblivious to that fact. You only see that after one million iterations, the Koch curve still comprise combination of line segments and points and therefore there would be always a point-line-point segment, e.g. there would be always a space between two points "not covered by a point." But after another couple of million iterations you find that this particular line segment is littered with vertex points as the bending continues. Go back and look at the example once again. Do you see any other point apart from the endpoints?

O_____________________M

No?
The conclusion is then that this line segment is not entirely covered by points. That also means that this line segment can't become the generator of the Koch curve, coz you can't locate the necessary inflection and vertex points to modify the line. The reason why you can't locate the points is the absence of any points between O and M. That in turn means that the finite length of the O_M line cannot be divided by number 3, coz the result of such a division looks like

O_______|_______|_______M

and since there are no points between O and M, there is no way to define and locate the points through (M - O)/3. The general consequence is that Organic Mathematics discovered numbers greater than zero that are indivisible. (Applause.)

BUT! The concept of the limit says that there is always a space between two points on a curve, otherwise there would be no derivative of the function that draws such a curve, and without us being able to compute derivatives, the science time would stop in the 16th century. The length of such a pointless segment approaches zero -- zero is the limit. So in this respect, it's true that "line cannot be entirely covered by points." On the other hand, any line length can be further divided. That's a contradiction that the concept of infinity solves. You can locate any point on a curve and at the same time compute the derivative of the function that draws the curve. The result in the approximate format would be "infinitely precise," but not "exact."

epix this is the second time that you agree with OM and does not agree with Traditional Math ( the first time was in http://forums.randi.org/showpost.php?p=6518481&postcount=12211 ), because Tradisional Math claims that a 1-dim space is totally covered by 0-dim spaces, such that 1/2+1/4+1/8+1/16+... = EXACTLY 1, where 1 is the limit.

PI is to EXACT as 3.1415... is to INFINITELY PRECISE

In other words, Do you agree that 3.1415...[base 10] < PI , as shown in http://forums.randi.org/showpost.php?p=6470162&postcount=12091 ?

Please answer to this question only by "Yes" or "No".

epix

5th November 2010, 07:48 PM

epix this is the second time that you agree with OM and does not agree with Traditional Math ( the first time was in http://forums.randi.org/showpost.php?p=6518481&postcount=12211 ), because Tradisional Math claims that a 1-dim space is totally covered by 0-dim spaces, such that 1/2+1/4+1/8+1/16+... = EXACTLY 1, where 1 is the limit.
Show me any text that says 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. You never provide any evidence of what you think mathematicians claim. It's very possible though that you'd come across that expression in the form of

∞
∑ 1/2k = 1
k=1

where the writer assumes that the infinity symbol above Sigma is a sufficient indication of 1 being the limit of the sum and not its exact result and skips the lim k → ∞ before Sigma.

It's remarkable to find out that you've brainwashed yourself into the state of irreversible belief about mathematicians being that stupid to believe that 1 + 2 + 3 + 4 + ... = "exact result".

In other words, Do you agree that 3.1415...[base 10] < PI , as shown in http://forums.randi.org/showpost.php?p=6470162&postcount=12091 ?

Please answer to this question only by "Yes" or "No".

No. According to OM, 0.999... = 1 (exact result).
0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1
http://forums.randi.org/showpost.php?p=6514794&postcount=12201

and therefore 3.1415... = Pi and not 3.1415... < Pi

You can't have it both ways, Doron. Just make up your mind and let me know when that happens.

How is that instrument that will multiply very small but finite numbers for OM going along? Are you finished devising or not? You can't collapse the world of traditional mathematics and render it no good without showing that the axe that went down knows how to multiply all numbers that live in R.

doronshadmi

6th November 2010, 04:27 AM

No. According to OM, 0.999... = 1 (exact result).

0.999... = 0.9 + 0.09 + 0.009 + ... + 0.000...1 = 1

Wrong conclusion since (0.999...[base 10] = 0.9[base 10] + 0.09[base 10] + 0.009[base 10] + ...) < (0.9[base 10] + 0.09[base 10] +
0.009[base 10] + ... + 0.000...1[base 10] = 1) by 0.000...1[base 10]

Show me any text that says 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. You never provide any evidence of what you think mathematicians claim.

It is not what I think and this is exactly what Traditional Math claims about the considered subject, for example:

Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%C2%B7_%C2%B7_%C2%B7

http://en.wikipedia.org/wiki/Absolute_convergence

Here is an evidence about 0.999... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/0.999...

It's remarkable to find out that you've brainwashed yourself into the state of irreversible belief about mathematicians being that stupid to believe that 1 + 2 + 3 + 4 + ... = "exact result".
On the contrary, OM claims that 1 + 2 + 3 + 4 + ... = "does not have an exact result"

Furthermore, OM claims that the cardinality of infinitely many distinct things "does not have an exact result", where Traditional Math (according to Cantor's reasoning) claims that the cardinality of infinitely many distinct things "has an exact result", like aleph0, 2^aleph0 , etc. ...

doronshadmi

6th November 2010, 10:35 AM

By the way, here is a nice program of Ford circles zoom in-out:

http://nrich.maths.org/public/viewer.php?obj_id=6594&part=index

epix

6th November 2010, 03:03 PM

It is not what I think and this is exactly what Traditional Math claims about the considered subject, for example:

Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%C2%B7_%C2%B7_%C2%B7

http://en.wikipedia.org/wiki/Absolute_convergence

Here is an evidence about 0.999... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/0.999...

That's not what traditional math claims; that's what pseudo mathematicians claim. Just look at the animated "informal proof" of the series in question. That's a complete joke. There are two kinds of professionals: those who know and those who understand. An appeal to authority obscures the distinction.

If you stick with the particular subject, then you find out that not all is well with the world of mathematics. Fortunately, certain "irregularities" occur as stuff is approaching infinity, and therefore there is no physical representation.

Look at this case: If you organize all real numbers in the ascending order, then the result can be very much likened to a line segment "completely covered by points." That includes numbers, such as a < 1, with one digit repeating after the radix ad infinitum. An example of such a number is

0.999...

Does such a number exist?

According to 0.999... = 1 that the Wiki contributor and others love so much, such a number doesn't exist and therefore the line R cannot be entirely covered by points, as OM says.

There is an algorithm called "long division." You need to put that under the magnifying glass. It starts with

1/3 = 0.333333333333333333333333333333333333333333333333 333333333333333333333333333333333:boggled:33333333 33333333333333:rolleyes:

How about inventing an expression that would indicate that nothing is going to change above? How about

1/3 = 0.333... ?

That leads to taking a close look at terms such as "exact" and "approximate." The initial proof of 0.999... = 1 relies on 1/9 = 0.111... Is it really so?

doronshadmi

7th November 2010, 04:49 AM

That's not what traditional math claims;
It is exactly what traditional math claims.

According to 0.999... = 1 that the Wiki contributor and others love so much, such a number doesn't exist and therefore the line R cannot be entirely covered by points, as OM says.
1) OM says that R is an incomplete collection of 0() dimensional spaces, which can't entirely cover 1() dimensional space.

2) OM says that accordinng to (1) there exists number 0999...[base 10] < 1 by number 0.000...1, where the ...1 part of 0.000...1 expresses the 1() dimensional spaces that is not covered by 0() dimensional spaces.

3) Traditional Math claims that 0.999...[base 10] is one of many other numerals that represent number 1, exactly because Traditional Math claims that 1() dimensional space entirely covered by points (by 0() dimensional spaces ).

laca

7th November 2010, 05:22 AM

doronshadmi

7th November 2010, 09:40 AM

Hey doron, sorry to barge in after so long, but any luck in publishing anything? No? Still no, after all those years? What's it been now, 10? Aw, sorry. But don't despair! Maybe, just maybe, if you keep it up long enough, you get a nice white jacket as a consolation prize. With sleeves! :D
Hey laca. Maybe, just maybe, if you keep it up long enough, your black tooth in your mouth will fall by itself, and you will be able cancel your appointment with your dentist and save the money for your shrink.http://farm2.static.flickr.com/1182/5154460003_f71d498947_t.jpg You can take epix with you if you fill lonley.

laca

7th November 2010, 11:25 AM

Hey laca. Maybe, just maybe, if you keep it up long enough, your black tooth in your mouth will fall by itself, and you will be able cancel your appointment with your dentist and save the money for your shrink.http://farm2.static.flickr.com/1182/5154460003_f71d498947_t.jpg

Oh, I've struck a nerve, haven't I?

You can take epix with you if you fill lonley.

I'm not sure what lonley is or how to fill it... Maybe you can enlighten me? Oh, wait...

But seriously, doron. Can you answer a few questions for me?

How much is 9/9?
How about 99/99?
7/9?
76/99?
n/9, where n <= 9

Now tell me, how much is 0,999....?

epix

7th November 2010, 02:50 PM

It is exactly what traditional math claims.
Here is an evidence about 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, according Traditional Math:

http://en.wikipedia.org/wiki/1/2_%2B..._%C2%B7_%C2%B7

http://en.wikipedia.org/wiki/Absolute_convergence

Your concept of evidence is based on a singular appeal to authority, even though in your case it's kind of different, coz you have taken on the traditional math armed with nothing but a snow ball.

Let's take a look at what traditional math has to say about the absolute convergence that is particular to the conclusion about the result of the sum:

In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite.
http://en.wikipedia.org/wiki/Absolute_convergence

A series [symbol] is said to converge absolutely if the series [symbol] converges, where [symbol] denotes the absolute value. If a series is absolutely convergent, then the sum is independent of the order in which terms are summed. Furthermore, if the series is multiplied by another absolutely convergent series, the product series will also converge absolutely.
http://mathworld.wolfram.com/AbsoluteConvergence.html

You see that the quote from Eric Weisstein at Wofram Research never mentions what Wiki claims about the finite sum. That's because not too many folks are capable of such an aggravated assault on common sense and grossly misdefine the meaning of the term "absolute convergence." Can't you understand that Wikipedia is a public encyclopedia and any idiot can edit it?

doronshadmi

7th November 2010, 10:53 PM

Oh, I've struck a nerve, haven't I?
Yes, the nerve of your black tooth.

laca

7th November 2010, 11:09 PM

Yes, the nerve of your black tooth.

Yeah, yeah. So, no answer? Come on, a man of your intellect can surely answer a couple of simple questions! You do remember how to do divisions from elementary school, don't you?

doronshadmi

8th November 2010, 09:18 AM

Can't you understand that Wikipedia is a public encyclopedia and any idiot can edit it?

Here is more stuff about this subject, according to Traditional Math:

http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

The Man

8th November 2010, 09:20 AM

The Man you have no case because you do not distinguish between the complex and the non-complex.

Doron “you have no case because you do not distinguish between” your fantasies and misconceptions (often apparently deliberate) from, well, mathematics.

Your dichotomist labels do not change the fact that a space is not independent of its sub-spaces.

You are talking about the dependency under the complex results among independent spaces.

No Doron I’m specifically talking about that fact that a space is not independent of its sub-spaces. That you simply want to talk about something else, once again your dichotomist labels, is simply your problem.

Let me give you an example:

The existence of 1-dim and 0-dim spaces are independent of each other, such that if one of them is missing, the other one still exists.

Once again a space is not independent of its sub-spaces, which, for a “1-dim” space, includes both “1-dim” and “0-dim spaces” as sub-spaces of that space. While a point, being zero dimensional, has no sub-spaces.

Now let's observe a complex like line-segment, which is the result of the linkage among 1() and 0().

“the result of the linkage among 1() and 0().” makes your “complex like line-segment” dependent on both Doron, by your own assertion.

Even if the length of 1() space under the complex, called line-segment, depends on the values of 0() spaces, it does not mean the 1() or 0() existence depend on each other.

Again, simply repeating your nonsense assertions from before does not change the fact that a space is not independent of its sub-spaces.

laca

8th November 2010, 09:22 AM

Hey, doron! Still no luck with that elementary math? Here it is again:

But seriously, doron. Can you answer a few questions for me?

How much is 9/9?
How about 99/99?
7/9?
76/99?
n/9, where n <= 9

Now tell me, how much is 0,999....?

If you want to, I could refresh your memory on how to do divisions.

doronshadmi

8th November 2010, 01:01 PM

“1-dim” space, includes both “1-dim” and “0-dim spaces” as sub-spaces of that space.

In other words, you show again your inability to distinguish between

∞(
1(),0()
)

and

∞(
1(0())
)

because you are a Total L0()ss case.

laca

8th November 2010, 01:17 PM

We can play this game too if you wish.

You can't get 9/9. Ha!

epix

8th November 2010, 03:01 PM

Here is more stuff about this subject, according to Traditional Math:

http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html
This time the traditional math is doing a good job explaining stuff to a 12th grader:

... and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

Note that the writer put the word value into the quotation marks. If you wonder why, follow the yellow line . . .

The writer didn't use the informal and strongly intuitive proof that the sum of the sequence in question is converging toward 2 but never reaches the number, as it obviously can't, but in this circumstance, let's refresh it using the original sequence you argued about that starts with 1/2.

1/2 = 1/2
1/2 + 1/4 = 3/4
1/2 + 1/4 + 1/8 = 7/8
1/2 + 1/4 + 1/8 + 1/16 = 15/16
1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 31/32

You can see that the result of the partial sums have always the form (denominator-1)/denominator, and this configuration will not change as there will be more and more addends whose number will be approaching infinity. In other words, there will never be a moment where suddenly the partial result of the sum will change into numerator = denominator with the result of exact 1.

It's very hard to believe that the "traditional mathematicians" would fail to ponder this kind of development and propose that the "result of the sum is exactly 1."

The Man

8th November 2010, 03:37 PM

In other words, you show again your inability to distinguish between

∞(
1(),0()
)

and

∞(
1(0())
)

because you are a Total L0()ss case.

Once again you simply show your inability to understand that a space is not independent of its sub-spaces.

epix

8th November 2010, 05:27 PM

Here is more stuff about this subject,

http://img580.imageshack.us/img580/241/bookbyd.png

doronshadmi

8th November 2010, 08:44 PM

http://img580.imageshack.us/img580/241/bookbyd.png

No epix, you have the joy to be against no matter what, why and how.

Here are the relevant part, taken from http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

It is this limit which we call the "value" of the infinite sum.

How do we find this value?

If we assume it exists and just want to find what it is, let's call it S. Now

S = 1 + 1/2 + 1/4 + 1/8 + · · ·
so, if we multiply it by 1/2, we get
(1/2) S = 1/2 + 1/4 + 1/8 + 1/16 + · · ·
Now, if we subtract the second equation from the first, the 1/2, 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1 which means S/2 = 1 and so S = 2.

...

In your example, the finite sums were

1 = 2 - 1/1
3/2 = 2 - 1/2
7/4 = 2 - 1/4
15/8 = 2 - 1/8

and so on; the nth finite sum is 2 - 1/2^n. This converges to 2 as n goes to infinity, so 2 is the value of the infinite sum.

1) Traditional Math explicitly uses = , such that S - (1/2)S = 1 which means S/2 = 1 and so S = 2

2) The term value is explicitly used at the end of the answer.

doronshadmi

8th November 2010, 08:51 PM

Once again you simply show your inability to understand that a space is not independent of its sub-spaces.

Once again your inability to distinguish between

∞(
1(),0()
)

and

∞(
1(0())
)

shows its trivial reasoning.

epix

8th November 2010, 11:18 PM

No epix, you have the joy to be against no matter what, why and how.

Here are the relevant part, taken from http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

1) Traditional Math explicitly uses = , such that S - (1/2)S = 1 which means S/2 = 1 and so S = 2

2) The term value is explicitly used at the end of the answer.
Yes. Unlike OM, math is using the symbol '=' often, coz it is essential to mathematics. But the symbol is always accompanied by various terms that '=' holds identical, and that escaped your attention. In the particular case above, the writer replied to a 12th grader under the assumption that if that person has made it to the 12th grade, he or she would be able to understand on the first reading what I highlighted in my next-to-last post, that is

It is this limit which we call the "value" of the infinite sum.

That sum S is the limit and not just the sum of the infinite sequence. In other words if Limit = S and S = 2 then Limit = 2. And, according to the definition translated for the slower students, the limit is a number that another number approaches but can't ever reach, the same way infinity can't be reached.

Here is an explanation of the limit to those who never heard such a word. The explanation stresses from the beginning that the limit can't be reached and it uses the full expressive means that don't omit any term, as it often happens in the mathematician-to-mathematician correspondence, which proved to be the source of a great deal of confusion to you.
http://www.themathpage.com/acalc/limits.htm

Of course, the explanation assumes a normal fetal development on the part of the reader . . .

Anders Lindman

8th November 2010, 11:52 PM

Doron, you are misusing common terms.
http://en.wikipedia.org/wiki/Information_entropy

I was thinking the same thing. According to information entropy the expansion of primes would have the highest entropy, not the lowest I think. For example if zip compression was used on the sets describing the expansion of numbers (see below), then the sets for the primes would be the least compressible probably (the more repetitive order the more compression).

2
---
{1,1}

3
---
{1,1,1}
{2,1}

4
---
{1,1,1,1}
{2,1,1}
{2,2}
{3,1}

5
---
{1,1,1,1,1}
{2,1,1,1}
{2,2,1}
{3,1,1}
{3,2}
{4,1}

6
--
{1,1,1,1,1,1}
{2,1,1,1,1}
{2,2,1,1}
{2,2,2}
{3,1,1,1}
{3,2,1}
{3,3}
{4,1,1}
{4,2}
{5,1}

7
---
{1,1,1,1,1,1,1}
{2,1,1,1,1,1}
{2,2,1,1,1}
{2,2,2,1}
{3,1,1,1,1}
{3,2,1,1}
{3,2,2}
{4,1,1,1}
{4,2,1}
{5,1,1}
{5,2}
{6,1}

...

doronshadmi

9th November 2010, 02:08 AM

Yes. Unlike OM, math is using the symbol '=' often, coz it is essential to mathematics. But the symbol is always accompanied by various terms that '=' holds identical, and that escaped your attention. In the particular case above, the writer replied to a 12th grader under the assumption that if that person has made it to the 12th grade, he or she would be able to understand on the first reading what I highlighted in my next-to-last post, that is

That sum S is the limit and not just the sum of the infinite sequence. In other words if Limit = S and S = 2 then Limit = 2. And, according to the definition translated for the slower students, the limit is a number that another number approaches but can't ever reach, the same way infinity can't be reached.

Here is an explanation of the limit to those who never heard such a word. The explanation stresses from the beginning that the limit can't be reached and it uses the full expressive means that don't omit any term, as it often happens in the mathematician-to-mathematician correspondence, which proved to be the source of a great deal of confusion to you.
http://www.themathpage.com/acalc/limits.htm

Of course, the explanation assumes a normal fetal development on the part of the reader . . .

Traditional Math is very clear about this subjecet, as written at the end of the answer (by using the term value and not "value").

http://www.math.toronto.edu/mathnet/questionCorner/geomsum.html

... so 2 is the value of the infinite sum.

By the way, http://www.themathpage.com/ARITH/bio.htm the writer of http://www.themathpage.com/acalc/limits.htm
is not a good example of Traditional professional mathematician.

This is how professional mathematicians understand this subject:

http://www.youtube.com/watch?v=o7GLWMXq7jo ( http://www.merlot.org/merlot/viewMember.htm;jsessionid=7585E9CEEA22E24FC6F2544E 69990553?id=26748 )

laca

9th November 2010, 02:18 AM

Hey doron, I understand that all the close-minded mathematicians don't want to read your gibberish. But for sure, you have found some application of your "theory", haven't you? Something like that would surely attract attention. Or posting on this forum is all you do? Doesn't that seem silly to you?

doronshadmi

9th November 2010, 02:28 AM

I was thinking the same thing. According to information entropy the expansion of primes would have the highest entropy, not the lowest I think. For example if zip compression was used on the sets describing the expansion of numbers (see below), then the sets for the primes would be the least compressible probably (the more repetitive order the more compression).

2
---
{1,1}

3
---
{1,1,1}
{2,1}

4
---
{1,1,1,1}
{2,1,1}
{2,2}
{3,1}

5
---
{1,1,1,1,1}
{2,1,1,1}
{2,2,1}
{3,1,1}
{3,2}
{4,1}

6
--
{1,1,1,1,1,1}
{2,1,1,1,1}
{2,2,1,1}
{2,2,2}
{3,1,1,1}
{3,2,1}
{3,3}
{4,1,1}
{4,2}
{5,1}

7
---
{1,1,1,1,1,1,1}
{2,1,1,1,1,1}
{2,2,1,1,1}
{2,2,2,1}
{3,1,1,1,1}
{3,2,1,1}
{3,2,2}
{4,1,1,1}
{4,2,1}
{5,1,1}
{5,2}
{6,1}

...
It depends on the interpretation of collections of distinct and non-distinct elements.

In my model, more distinction is less entropy, and less distinction is more entropy.

Prime numbers are characterized by more distinction among the elements of a given partition, and therefore they are characterized by less entropy.

For example if zip compression was used on the sets describing the expansion of numbers (see below), then the sets for the primes would be the least compressible probably (the more repetitive order the more compression).
You are right, the sets for the primes would be the least compressible and therefore have the least entropy.

epix

9th November 2010, 03:26 AM

Traditional Math is very clear about this subjecet, as written at the end of the answer (by using the term value and not "value").
You need to understand something about how the quotation marks are used in this case. The writer didn't quote anyone by putting the word value into the quotation marks; the writer used them to indicate the as if that the quotation marks are sometimes used for. After that, the quotation marks are no longer required if the word is repeated. Remember that the writer is replying to a 12th grader who writes essays and knows English grammar well. You picked up an example of mathematician-to-nonmathematician correspondence as an example of what traditional math claims, but that may not work well with you due to the informality of the text that isn't written in your native language. It's the Catch 22: If you pick up the mathematician-to-mathematician text instead to demonstrate alleged fallacies, then you are likely to misinterpret it, coz you are not a "traditional mathematician."

By the way, http://www.themathpage.com/ARITH/bio.htm the writer of http://www.themathpage.com/acalc/limits.htm
is not a good example of Traditional professional mathematician.
Really? What seems to be the problem?

doronshadmi

9th November 2010, 04:07 AM

You need to understand something about how the quotation marks are used in this case.

No epix, you need to understand something about how the quotation marks are not used at the final part of this case, exactly as shown in http://forums.randi.org/showpost.php?p=6532043&postcount=12241 .

This time please look at this movie which shows how professional mathematicians understand this subject:

http://www.youtube.com/watch?v=o7GLWMXq7jo ( http://webalt.math.helsinki.fi/content/about/people/seppala/index_eng.html )

Really? What seems to be the problem?
He does not have a Ph.D in Mathematics.

Anders Lindman

9th November 2010, 04:15 AM

It depends on the interpretation of collections of distinct and non-distinct elements.

In my model, more distinction is less entropy, and less distinction is more entropy.

Prime numbers are characterized by more distinction among the elements of a given partition, and therefore they are characterized by less entropy.

You are right, the sets for the primes would be the least compressible and therefore have the least entropy.

Maybe I see what you mean. That the less distinction there is the more 'noise' there is, which is a form of disorder which in turn is related to entropy.

It depends on how entropy is defined I guess. Using Shannon entropy (http://en.wikipedia.org/wiki/Entropy_(information_theory)), the less compressible some information is, the more Shannon entropy it has.