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becomingagodo · 14th November 2007, 09:53 AM

I made one long post, however I couldn't post.

Well, I will make it shorter. And try again.

I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me.

So I would like to discuss some of my thought expriments.

Taking away the infinte small pieces.

Can you take away a infinte small piece and then continue to get zero. The anwser is no. You takeaway one then another, however their would also be infinte left i.e. N-1 equals N.
However, what if you take away infinte at once. This does the trick, you have infinte small pieces and then you grab all of them at once and then
N-N=0. So we have a object that you cannot add things to or takeaway infinte small piece and change it.

This concept is handy when it comes to calculus

Because

y=x^2
y+dy=(x+dx)^2
y+dy= x^2 + 2xdx + dx^2
dy/dx= 2x + dx
however, above thought expriments shows dx does nothing
so
Lim dy/dx= 2x
x to 0

Again, thats how I think all the time. I can give more example, however their is something wrong with my computer and it is hard to post and I need to get off now, however I will post more later.

I don't like a particular branch of mathematics if they don't involve any infinties. However, in some way all branches of mathematics have infinty in them, so to truely understand infinty you must understand mathematics. Infinty is one of the main reasons I don't give up mathematics as thought expriments on infinty is really insightful. The other improtant concept I feel is complexity i.e. chaos theory and fractals.

Oh yeah, another thought expriment

Look at a cake, now divide it by zero. How? Now diving is just adding to something like 9/3=3 as you add 3 threes to get nine. Lets call the cake 1. Now add zero to get one.
This may sound absurd, however we know that dx tends to 0 so it most also be true that 0 tends to dx. So now we add infinty small bit to get one.

However, let change the process instead we have one and we take away infintly small pieces, this can't be done. However, it can be done when take away the infintly small pieces at once, which their is infinte. So 1/0=N

In equation form it would be

Lim 1/0=N
x to 0

However, I am assuming that multiplication is correct, I would like to know what happens when instead of considering real numbers we use quaternion or something else, you know when the order of multiplication matters.

Darth Rotor · 14th November 2007, 10:00 AM

Originally Posted by becomingagodo

I made one long post, however I couldn't post.

I think you posted twice.

Was that part of your experiment?

Quote:

I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me.

So I would like to discuss some of my thought expriments.

Taking away the infinte small pieces.

That would remove what is left of your ability to express yourself in written form. That opening paragraph is enough to induce vomiting.

DR

drkitten · 14th November 2007, 10:53 AM

Originally Posted by becomingagodo

I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me.

No, I understand you quite well. Your ability to express yourself is appallingly bad, but the underlying question is a quite sophisticated one.

Quote:

Can you take away a infinte small piece and then continue to get zero. The anwser is no. You takeaway one then another, however their would also be infinte left i.e. N-1 equals N.
However, what if you take away infinte at once. This does the trick, you have infinte small pieces and then you grab all of them at once and then
N-N=0. So we have a object that you cannot add things to or takeaway infinte small piece and change it.

This is more or less the problem that mathematicians struggled with between Newton and Weierstrass; the way to formalize the idea of meaningful mathematical manipulations of the infinitely small. How can you add the infinitely small to something and effect a change? Can you even have two differently-sized infinitely small quantities? How can they be compared? Et cetera.

Unfortunately, you appear to have misunderstood what the concept of a 'limit' actually entails.

Quote:

y=x^2
y+dy=(x+dx)^2
y+dy= x^2 + 2xdx + dx^2
dy/dx= 2x + dx

So far, okay. (You don't understand the notation, but,... whatever.)

Quote:

however, above thought expriments shows dx does nothing

... if you treat dx directly. That's why you need to use the limit process.

Let's assume that dx is very small but not infinitely so. Say, 0.0001. Well, dy/dx is therefore 2x + 0.0001. If dx were even smaller, say 0.0000001, dy/dx would be even closer to 2x (it would be 2x + 0.0000001). If we let dx get "sufficiently close" to zero, then dy/dx will be "sufficiently close" to 2x.

The "limit" is not just a replacement, but an examination of trends.

Quote:

Infinty is one of the main reasons I don't give up mathematics as thought expriments on infinty is really insightful.

Not when you get the wrong insight, unfortunately.

The other improtant concept I feel is complexity i.e. chaos theory and fractals.

[QUTOE]
Look at a cake, now divide it by zero. How? Now diving is just adding to something like 9/3=3 as you add 3 threes to get nine. Lets call the cake 1. Now add zero to get one.
This may sound absurd, however we know that dx tends to 0 so it most also be true that 0 tends to dx. So now we add infinty small bit to get one.

However, let change the process instead we have one and we take away infintly small pieces, this can't be done. However, it can be done when take away the infintly small pieces at once, which their is infinte. So 1/0=N

In equation form it would be

Lim 1/0=N
x to 0[/quote]

No. 1/0 is a constant expression and is undefined. The limit of "undefined" is also undefined.

I think what you wanted to write was

Lim 1/x = N
x to 0

But even this isn't valid. What's "N"? It has no value.

What you can observe is that as x gets closer and closer to 0, the quantity 1/x gets larger and larger (closer and closer to infinity, if you want to look at it that way). So as x gets closer to 0, 1/x grows without bound. Depending upon where you studied mathematics, you can either claim that it therefore has no limit (that's what "infinite" means -- without bound or without limit), or that the limit is "infinity."

More generally, if you divide a single cake into pieces, each piece is 1/x of a cake. If you let the pieces get smaller and smaller, then the total number of pieces grows without bound. If you divide two cakes into x pieces, you get the same effect (each piece is 2/x of a cake)-- but the total amount of cake remains one or two cakes, depending upon what you started with. What you can't do (in "conventional"/A-level mathematics ) is divide a single cake into N pieces and reassemble those pieces to make two cakes. (Complexity, just shut up about Banach-Tarski, please....)

becomingagodo · 14th November 2007, 11:39 AM

Oh yeah, I understand know. Espically what our limits. Thanks drkitten.

I will think somemore and post some more thought expriments.

However, can someone explain this

You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999...
How is this possible?
Either it measures 1 or 0.999.. however if they are equal.
With abit of algebra
x=0.999...
10x=9.999...
10-1x=9
9x=9
x=9/9=1
What happened?
Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits?

drkitten · 14th November 2007, 11:50 AM

Originally Posted by becomingagodo

However, can someone explain this

You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999...

Oh, God, not this chestnut again.

Quote:

How is this possible?
Either it measures 1 or 0.999.. however if they are equal.
With abit of algebra
x=0.999...
10x=9.999...
10-1x=9
9x=9
x=9/9=1
What happened?

Exactly what you expect. You showed that the two expressions are indistinguishable via algebraic manipulation. By Leibniz's principle, they are therefore the same.

Quote:

Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits?

But what does the phrase "infinitely small difference" mean (mathematically speaking)?

The proper way of looking at it in terms of limits is to actually apply limits. The expression 0.9999999... does not actually denote a number per se; it denotes the limit of a sequence like 0.9, 0.99, 0.999, 0.9999, and so forth. (This kind of sequence is sometimes called a Cauchy sequence after the guy who formalized it.) I claim (and it's fairly easy to prove) that as the number gets longer and longer, the number gets "closer and closer" to 1.0. Hence, although the values themselves are distinct from 1, the limit of the values is 1.0 exactly.

Since the value of the infinite expression is defined as the value of the limit, the infinite expression has the value 1.0.

Cosmo · 14th November 2007, 04:57 PM

Originally Posted by becomingagodo

You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999...
How is this possible?
Either it measures 1 or 0.999.. however if they are equal.
With abit of algebra
x=0.999...
10x=9.999...
10-1x=9
9x=9
x=9/9=1
What happened?
Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits?

Try it this way.

x = 1/3
1/3 = 0.3333333..

But, 3x = 1

Therefore, 3(0.333333..) = 1

...and, yeah, drkitten's explanation too.

Dorian Gray · 14th November 2007, 08:44 PM

Expriments?

slingblade · 14th November 2007, 09:15 PM

Originally Posted by Dorian Gray

Expriments?

Don't. You'll only hurt yourself, and regret it in the morning. Right after you chew off your own arm.

Back away slowly.

14th November 2007, 09:53 AM	#1
becomingagodo Banned Join Date: Mar 2007 Posts: 698	Thought expriments I made one long post, however I couldn't post. Well, I will make it shorter. And try again. I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me. So I would like to discuss some of my thought expriments. Taking away the infinte small pieces. Can you take away a infinte small piece and then continue to get zero. The anwser is no. You takeaway one then another, however their would also be infinte left i.e. N-1 equals N. However, what if you take away infinte at once. This does the trick, you have infinte small pieces and then you grab all of them at once and then N-N=0. So we have a object that you cannot add things to or takeaway infinte small piece and change it. This concept is handy when it comes to calculus Because y=x^2 y+dy=(x+dx)^2 y+dy= x^2 + 2xdx + dx^2 dy/dx= 2x + dx however, above thought expriments shows dx does nothing so Lim dy/dx= 2x x to 0 Again, thats how I think all the time. I can give more example, however their is something wrong with my computer and it is hard to post and I need to get off now, however I will post more later. I don't like a particular branch of mathematics if they don't involve any infinties. However, in some way all branches of mathematics have infinty in them, so to truely understand infinty you must understand mathematics. Infinty is one of the main reasons I don't give up mathematics as thought expriments on infinty is really insightful. The other improtant concept I feel is complexity i.e. chaos theory and fractals. Oh yeah, another thought expriment Look at a cake, now divide it by zero. How? Now diving is just adding to something like 9/3=3 as you add 3 threes to get nine. Lets call the cake 1. Now add zero to get one. This may sound absurd, however we know that dx tends to 0 so it most also be true that 0 tends to dx. So now we add infinty small bit to get one. However, let change the process instead we have one and we take away infintly small pieces, this can't be done. However, it can be done when take away the infintly small pieces at once, which their is infinte. So 1/0=N In equation form it would be Lim 1/0=N x to 0 However, I am assuming that multiplication is correct, I would like to know what happens when instead of considering real numbers we use quaternion or something else, you know when the order of multiplication matters.
becomingagodo Banned Join Date: Mar 2007 Posts: 698	Last edited by becomingagodo; 14th November 2007 at 10:14 AM.

14th November 2007, 10:00 AM	#2
Darth Rotor Salted Sith Cynic Join Date: Aug 2006 Location: Rat cheer Posts: 34,379	Originally Posted by becomingagodo I made one long post, however I couldn't post. I think you posted twice. Was that part of your experiment? Quote: I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me. So I would like to discuss some of my thought expriments. Taking away the infinte small pieces. That would remove what is left of your ability to express yourself in written form. That opening paragraph is enough to induce vomiting. DR
	__________________ Helicopters don't so much fly as beat the air into submission. "Jesus wept, but did He laugh?"--F.H. Buckley____"There is one thing that was too great for God to show us when He walked upon our earth ... His mirth." --Chesterton__"If the barbarian in us is excised, so is our humanity."--D'rok__ "I only use my gun whenever kindness fails."-- Robert Earl Keen__"Sturgeon spares none.". -- The Marquis Last edited by Darth Rotor; 14th November 2007 at 10:04 AM.

14th November 2007, 11:39 AM	#4
becomingagodo Banned Join Date: Mar 2007 Posts: 698	Oh yeah, I understand know. Espically what our limits. Thanks drkitten. I will think somemore and post some more thought expriments. However, can someone explain this You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999... How is this possible? Either it measures 1 or 0.999.. however if they are equal. With abit of algebra x=0.999... 10x=9.999... 10-1x=9 9x=9 x=9/9=1 What happened? Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits?
becomingagodo Banned Join Date: Mar 2007 Posts: 698

14th November 2007, 04:57 PM	#6
Cosmo Radioactive Rationalist Join Date: Jul 2004 Location: San Francisco, CA Posts: 1,169	Originally Posted by becomingagodo You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999... How is this possible? Either it measures 1 or 0.999.. however if they are equal. With abit of algebra x=0.999... 10x=9.999... 10-1x=9 9x=9 x=9/9=1 What happened? Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits? Try it this way. x = 1/3 1/3 = 0.3333333.. But, 3x = 1 Therefore, 3(0.333333..) = 1 ...and, yeah, drkitten's explanation too.
	Last edited by Cosmo; 14th November 2007 at 04:58 PM.

14th November 2007, 08:44 PM	#7
Dorian Gray Hypocrisy Detector Join Date: Nov 2002 Location: Dayton, Ohio Posts: 20,210	Expriments?
	__________________ "A little nonsense now and then is relished by the wisest men." - Willy Wonka "Rational arguments don't work on religious people. If they did, there wouldn't be any religious people." - House Additionally to Carlin being funnier than Izzard, I think Dorian is funnier than the Marquis. - Ron Tomkins

14th November 2007, 10:53 AM	#3
drkitten Penultimate Amazing Join Date: Mar 2004 Location: Wits' End Posts: 21,647	Originally Posted by becomingagodo I use thought expriments and when I use thought expriment I only consider the possibillity that are not obvious. I don't think normally, that where the confusion is proberly steming from, unless you think like me you can't understand me. No, I understand you quite well. Your ability to express yourself is appallingly bad, but the underlying question is a quite sophisticated one. Quote: Can you take away a infinte small piece and then continue to get zero. The anwser is no. You takeaway one then another, however their would also be infinte left i.e. N-1 equals N. However, what if you take away infinte at once. This does the trick, you have infinte small pieces and then you grab all of them at once and then N-N=0. So we have a object that you cannot add things to or takeaway infinte small piece and change it. This is more or less the problem that mathematicians struggled with between Newton and Weierstrass; the way to formalize the idea of meaningful mathematical manipulations of the infinitely small. How can you add the infinitely small to something and effect a change? Can you even have two differently-sized infinitely small quantities? How can they be compared? Et cetera. Unfortunately, you appear to have misunderstood what the concept of a 'limit' actually entails. Quote: y=x^2 y+dy=(x+dx)^2 y+dy= x^2 + 2xdx + dx^2 dy/dx= 2x + dx So far, okay. (You don't understand the notation, but,... whatever.) Quote: however, above thought expriments shows dx does nothing ... if you treat dx directly. That's why you need to use the limit process. Let's assume that dx is very small but not infinitely so. Say, 0.0001. Well, dy/dx is therefore 2x + 0.0001. If dx were even smaller, say 0.0000001, dy/dx would be even closer to 2x (it would be 2x + 0.0000001). If we let dx get "sufficiently close" to zero, then dy/dx will be "sufficiently close" to 2x. The "limit" is not just a replacement, but an examination of trends. Quote: Infinty is one of the main reasons I don't give up mathematics as thought expriments on infinty is really insightful. Not when you get the wrong insight, unfortunately. The other improtant concept I feel is complexity i.e. chaos theory and fractals. [QUTOE] Look at a cake, now divide it by zero. How? Now diving is just adding to something like 9/3=3 as you add 3 threes to get nine. Lets call the cake 1. Now add zero to get one. This may sound absurd, however we know that dx tends to 0 so it most also be true that 0 tends to dx. So now we add infinty small bit to get one. However, let change the process instead we have one and we take away infintly small pieces, this can't be done. However, it can be done when take away the infintly small pieces at once, which their is infinte. So 1/0=N In equation form it would be Lim 1/0=N x to 0[/quote] No. 1/0 is a constant expression and is undefined. The limit of "undefined" is also undefined. I think what you wanted to write was Lim 1/x = N x to 0 But even this isn't valid. What's "N"? It has no value. What you can observe is that as x gets closer and closer to 0, the quantity 1/x gets larger and larger (closer and closer to infinity, if you want to look at it that way). So as x gets closer to 0, 1/x grows without bound. Depending upon where you studied mathematics, you can either claim that it therefore has no limit (that's what "infinite" means -- without bound or without limit), or that the limit is "infinity." More generally, if you divide a single cake into pieces, each piece is 1/x of a cake. If you let the pieces get smaller and smaller, then the total number of pieces grows without bound. If you divide two cakes into x pieces, you get the same effect (each piece is 2/x of a cake)-- but the total amount of cake remains one or two cakes, depending upon what you started with. What you can't do (in "conventional"/A-level mathematics ) is divide a single cake into N pieces and reassemble those pieces to make two cakes. (Complexity, just shut up about Banach-Tarski, please....)

14th November 2007, 11:50 AM	#5
drkitten Penultimate Amazing Join Date: Mar 2004 Location: Wits' End Posts: 21,647	Originally Posted by becomingagodo However, can someone explain this You have a object that is 0.999.... then you measure the object, you should get either 1 or 0.999...., however 1=0.999... Oh, God, not this chestnut again. Quote: How is this possible? Either it measures 1 or 0.999.. however if they are equal. With abit of algebra x=0.999... 10x=9.999... 10-1x=9 9x=9 x=9/9=1 What happened? Exactly what you expect. You showed that the two expressions are indistinguishable via algebraic manipulation. By Leibniz's principle, they are therefore the same. Quote: Hypothetically speaking you could say that their is a infintly small difference that tends to 0, and then reverse the argument. However, how is the proper way off seeing this happening in terms of limits? But what does the phrase "infinitely small difference" mean (mathematically speaking)? The proper way of looking at it in terms of limits is to actually apply limits. The expression 0.9999999... does not actually denote a number per se; it denotes the limit of a sequence like 0.9, 0.99, 0.999, 0.9999, and so forth. (This kind of sequence is sometimes called a Cauchy sequence after the guy who formalized it.) I claim (and it's fairly easy to prove) that as the number gets longer and longer, the number gets "closer and closer" to 1.0. Hence, although the values themselves are distinct from 1, the limit of the values is 1.0 exactly. Since the value of the infinite expression is defined as the value of the limit, the infinite expression has the value 1.0.

14th November 2007, 09:15 PM	#8
slingblade Guest Join Date: Jul 2005 Posts: 23,642	Originally Posted by Dorian Gray Expriments? Don't. You'll only hurt yourself, and regret it in the morning. Right after you chew off your own arm. Back away slowly.
slingblade Guest Join Date: Jul 2005 Posts: 23,642