Y the vast majority of people on here r wrong and ought to hang their heads in sham

[Interesting Ian]

I've had almost no mathematical education at all. And yet I understand the following puzzle in contrast to all these mathematical geeks on here who don't understand it and think I'm incorrect! :rolleyes: LMAO!

OK, it concerns the thread Am I in error or LW? (http://www.randi.org/vbulletin/showthread.php?s=&threadid=36384)

Due to the fact that I know very little mathematical terms at all, I'll have to explain it mainly in English.

What I'm considering here is a series of random digits from 0 to 9. By series I mean one after the other such as for example:

1, 2, 3 . .etc.

I am not specifying how long such a sequence will be.

By random I mean that each and every digit has an equal chance of occurring next in the sequence, namely 1/10th.

Thus, for example we could have 491884903268 . . .

Now I'm considering the probability of some shorter sequence of numbers occurring in the longer series. This shorter sequence is specified. Now it really doesn't matter what digits constitute the shorter sequence of numbers, or how long the sequence is. It could be a million digits, or it could be one digit. For a sake of simplicity, let's suppose this shorter sequence of numbers just consists of one digit. Let's say it is "5".

Now we're asking what the probability of the shorter sequence of numbers occurring in the larger. So in this instance we're asking what is the chance of 5 appearing in this longer series.

Now we can alter the length of this longer series at will. In practise, what we will do, is start from a series of one digit, and keep increasing it until, and if, the specified shorter series of digits will occur in it (ie when 5 occurs in it).

The question we're seeking to answer is whether it is probabilistically possible whether the requisite number, ie "5", will never occur in the sequence, no longer how long we make it.



So with one digit in the longer series the probability is 90% that 5 will not occur.

With 2 digits it is 81%.

With 3 digits it is 73.9%

But in order to be probabilistically impossible it needs to be 0%.

So we go on, and on, and on, and on.

We can get down to 0.1% by adding enough digits.

Or 0.0001%

Or 0.0000000000000000001%

But still this is a finite, albeit an incredibly small probability.

But we can keep on adding more and more digits. With each digit added, the probability gets yet lower.

Note this process never stops. If the 5 doesn't turn up we can always add more digits and the probability of 5 not having turned up continually gets lower, and lower, and lower.

So how low can it go? Can it reach 0 and thus refute the thesis it is possible it will never occur?

My opponents say no, but I say it can.

First of all it should be made clear that infinitely close to 0, or unlimitedly close to 0 is exactly 0. I do not believe anyone does, or could deny this.

So we need simply show that as we keep adding digits we get unlimitedly close to 0.

Well, by continually adding digits we simply get lower and lower. But how low can it go? One point made by my opponents is that the rate at which the probability is diminishing is slowing down. Eventually adding a googolplex of digits will hardly make it go any lower at all. Nevertheless, with each digit added, it will get lower, even if by only a very small amount.

But yes, the rate of getting lower is drastically slowing down. Now crucially, what this means is that it is approaching a limit which it cannot cross. What is this limit? Why it is the limit of 0 probability itself!

But my opponents now have a dilemma. They cannot admit that the probability is getting unlimitedly close to zero, because that means that is to concede defeat!

So what can they do? Well they can say it is not approaching zero, but rather some other number. But this is clearly impossible to maintain, or if they think otherwise, what number might this be??

But now they're in an impossible position, because they have to admit that the probability is getting lower and lower as more digits are added, yet it's not reaching any limit!

Either it reaches a limit which must be zero, in which case they admit that the probability gets unlimitedly close to zero, which is none other than zero, or they have to say, at some stage, despite adding more digits, the probability doesn't get any lower at all! But this is nonsensical, and even if it weren't then what is this probability??

We have demonstrated that it is not possible for 5 never to occur because the possibility of it never occurring is unlimitedly close to zero, which is zero!

Simple.

Now, anyone disagree? Agree?

[gnome]

I believe I can address this,

Yes, the probability is approaching zero.

But, you are attempting to draw from that the conclusion that "5" must exist somewhere in the sequence. That may seem intuitively true, but of course something more rigorous must be developed.

Instead, I will try to prove the opposite, that the number "5" is never forced to appear in the sequence.

Let us state your proposition this way: that there is a number "n" at which the number 5 must have appeared in that position or sooner. It doesn't quite sound like your proposition, but if you follow the proof I think you'll find that this is what you're essentially saying.

My own contradiction follows:

Premise 1: At n=1, there exists a random sequence that doesn't contain contains a "5" until at least the second position.

Premise 2: For every n greater than 1, there exists a sequence that doesn't contain a "5" until position n+1 or further.

By mathematical induction, there is no n at which the number 5 must have appeared in that position or sooner.

So since no position "n" offered need ever bear fruit, so to speak, it can be said that it is possible for the sequence not to contain "5".

[Interesting Ian]

Originally posted by gnome
[B]I believe I can address this,

Yes, the probability is approaching zero.

But, you are attempting to draw from that the conclusion that "5" must exist somewhere in the sequence. That may seem intuitively true, but of course something more rigorous must be developed.



I've just proved it. Where is my error??



Instead, I will try to prove the opposite, that the number "5" is never forced to appear in the sequence.

Let us state your proposition this way: that there is a number "n" at which the number 5 must have appeared in that position or sooner.


What position?





It doesn't quite sound like your proposition, but if you follow the proof I think you'll find that this is what you're essentially saying.

My own contradiction follows:

Premise 1: At n=1, there exists a random sequence that doesn't contain contains a "5" until at least the second position.

Premise 2: For every n greater than 1, there exists a sequence that doesn't contain a "5" until position n+1 or further.

By mathematical induction,



What's "mathematical induction"?



there is no n at which the number 5 must have appeared in that position or sooner.



How does that follow from any of the foregoing??



So since no position "n"



"position"?? I thought n was a number.



offered need ever bear fruit, so to speak, it can be said that it is possible for the sequence not to contain "5".

I have no idea how you conclude this. Your "argument" is gobbledegook. I repeat. Where is the error in my argument?? :rolleyes:

[scribble]

It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

[Cecil]

I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

[scribble]

Originally posted by Cecil
I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

Evidence shows the probability of him understanding any given proposition is pretty slim. Infinitesimal, perhaps.

[Tricky]

Starting a new thread won't change anything, Ian. You're still wrong. You haven't proven anything. You've asserted it, and incorrectly at that. You are truly a person who could say, "I don't know math from a hole in the ground."

[Cleopatra]

Originally posted by Tricky
Starting a new thread won't change anything, Ian. You're still wrong. You haven't proven anything. You've asserted it, and incorrectly at that. You are truly a person who could say, "I don't know math from a hole in the ground."

He started this thread at 4:20 AM. You can imagine.... Maybe you should leave him to sober up first.

[Cecil]

Originally posted by scribble
Evidence shows the probability of him understanding any given proposition is pretty slim. Infinitesimal, perhaps. ExAyAz ((UnderstandingOf(y,z) > UnderstandingOf(x,z)) /\ UnderstandingOf(x,x) = 0)

(Pretend the E is backwards and the As are upside down)

Proof? Look at the third post in this thread.

[epepke]

Originally posted by Interesting Ian
I've had almost no mathematical education at all. And yet I understand the following puzzle in contrast to all these mathematical geeks on here who don't understand it and think I'm incorrect! :rolleyes: LMAO!

The first part is clear, that you've had almost no mathematical education at all.

To your credit, though, you've hit on one of the problems that we math geeks like to use in an attempt to learn more about math.

I'll try to avoid too much mathematical language. bit here has to be some. I'll try to remember to italicize the funny bits. Mathematics, or at least this branch, deals with rings, groups, and algebras. There are technical differences, but basically, they all consist of some numbers and some operators. Mathematics consisits of looking at how they work, or rather, what you can show about how they work, given basic assumptions.

Some of the interesting properties that mathematicians look for include associativity, commutativity, and most importantly here, closure.

For example, let's take the ring consisting of the natural numbers (1, 2, 3, 4, 5, and so on) and the operations + and *. We can say that this is a commutative ring which is closed over + and *, because if you apply either of the operators over a member of the set of numbers, you get another member of the set. (Ring implies other stuff too, but it isn't important here.)

However, the set of natural numbers obviously isn't closed over subtraction (-), because 3 - 7 isn't a natural number. So we come up with the set of integers, which may be negative or zero as well as positive. This solves the problem of subtraction, but it doesn't solve the problem of division, because 3/7 is not an integer. So we come up with rational numbers. That doesn't solve the problem with square root, so we come up with real numbers, which helps a bit, but not with the square root of negative numbers. So we come up with complex numbers. And this solves most problems of closure, except for 1/0 and 0/0.

This is probably the limit of most people's education, but there's more. Lots more.

So, in your paradox, you're using probability. That's fine. It's usually defined over the real interval [0..1], but it's also possible to define consistent probabilistic systems over all real numbers. Or over the complex numbers or some range thereof. (That's where it ends for probability; the rules stop working beyond that.) But all we really need are the real numbers here, with the provision that we're only interested in a range. So far, so good.

So, you introduce a string of digits. As long as it is of finite length, it's fine. The set of operations associated with probability are closed over strings of digits. Great.

Now, there's a trick for avoiding going beyond real numbers or strings of digits. We can say that as the string of digits approaches infinity, the probability approaches zero. That's a limit. Some people call this "infinitessimal," which effectively means "close enough to 0 that you might as well stop worrying about it."

But what is it really? Let's say we have a string of digits that doesn't just approach but really is infinitely long. We can pretend this; we're not constrained to the real world. We could imagine some sort of magical machine (there's an actual name: oracle) which produces one digit in a half second, the next digit in a quarter second, and so on and so forth and let it run forever.

This would result in a probability of 1/infinity of not seeing a 5 somewhere. Which, based on intuition, would be identically 0 i the real numbers. However, as you have correctly pointed out, it might be that there is no 5. That seems a paradox.

However, our intuition would be wrong. 1/infinity is not a real number. Infinity itself is not a real number. So what the hell is it?

Well, it's a number with these properties. There are numbers that are not greater than it but not less than 0. However, it is less than any such number but not less than 0. In the set of real numbers, we'd have to conclude that it was, identically, 0. But it isn't in that set. The set it's in has to be a set in which the operators >, <, <=, and >= don't work the way they do with real numbers.

Some people have played with extending the concept of real numbers to include these things. They are sometimes called "hyperreals."

I could also write this number in Cantor's transfinite notation as 10^-omega. But that's a whole 'nother can of worms.

[The Central Scrutinizer]

I haven't even followed the issue, but I went on over to the poll and voted for LW. Because II has demonstrated on numerous occasions that he isn't the brightest bulb in the box, so I just assume he is wrong again.

[scribble]

Originally posted by The Central Scrutinizer
I haven't even followed the issue, but I went on over to the poll and voted for LW. Because II has demonstrated on numerous occasions that he isn't the brightest bulb in the box, so I just assume he is wrong again.

Gee whiz, TCS, you're not much of a skeptic. Read through his claim once, THEN vote. It won't take long.

[scribble]

epepke, that, sir, is a killer post. Excellent explanation. I wonder if going even higher-level is going to help Ian.

[Cleopatra]

Originally posted by scribble
epepke, that, sir, is a killer post. Excellent explanation. I wonder if going even higher-level is going to help Ian.

Yes indeed!!! I realized of what the discussion was about. :)

No it' won't help Ian but it will help the bystanders!!

I have been telling you. In this forum we owe a lot to Ian.

[scribble]

Originally posted by Cleopatra

I have been telling you. In this forum we owe a lot to Ian. [/B]

I said as much in the other thread. Sadly, the lot we owe to him is about the same we'd owe a clever random text generator.

[The Central Scrutinizer]

Originally posted by scribble


Gee whiz, TCS, you're not much of a skeptic. Read through his claim once, THEN vote. It won't take long.

I would, but it's my night to sort the sock drawer.

[The Don]

Once again Ian, you have demonstrated a lack of understanding of (what used to be called 'O' level) mathematics. What you have said would SEEM to be intuitively true, but unfortunately it isn't.

You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0. Intuitively this would seem to be the case but in order to make it happen you had to insist that the set of numbers you chose would be chosen only by you.

The problem with introducing the concept of infinity into any intuitive understanding of a situation is that it behaves in strange ways. When talking about an infinitely long string of characters, most of us would think of something, say 1,000 or 1,000,000 characters long. To misquote Douglas Adams "Infinity is much bigger that that".

To demonstrate how wrong you are......

What happens when the string for which you are searching is only one character shorter than the string in which you're searching ? Or two characters, or three. It's not so certain that the string 345 will turn up in any four digit number is it ?

All other cases are just versions of the same situation albeit the difference in the lengths of strings is greater...

[T'ai Chi]

Originally posted by Interesting Ian

So in this instance we're asking what is the chance of 5 appearing in this longer series.


Just to clarify since this changes the problem mathematically somewhat, are you interested in the total number of times '5' occurs in the sequence, or just the first time a '5' occurs?

[epepke]

Originally posted by scribble
epepke, that, sir, is a killer post. Excellent explanation.

Thank you, sir. Although rereading it I can find a few ugly statements, I'll clarify them if challenged. Like that the oracle machine's forever is really just a second for us. And I wasn't clear that I was talking about the membership of 1/infinity in the set of real numbers. It could have used a better edit than I gave it.

I wonder if going even higher-level is going to help Ian.

Let's not try to do too much right off the bat. We don't even know yet if Ian is actually interested, as opposed to just asserting that he's smarter than everyone. I haven't even had to talk about Peano arithmetic at the low end or Cantor's diagonal proof at the middle. Let alone how much fun you can have by in general using elements of a set to label elements of a set.

[Zep]

Would it be fair to say that Ian has confused the idea that a given digit MUST occur in a string of digits of arbitrary length, as opposed to the PROBABILITY that it will occur in that same string?

[epepke]

Originally posted by The Don
You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0. Intuitively this would seem to be the case but in order to make it happen you had to insist that the set of numbers you chose would be chosen only by you.

I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

[The Don]

Originally posted by epepke


I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

As I remember it, the conversation went something like this:

II: I play a set of numbers in the UK lottery. These numbers frequently have a > 100% payback chance. I took this to mean that the return * odds / stake was > 1

In the UK lottery, the odds against winning the jackpot are 14,000,000 ish to one

A little less than 50 % of stake money goes into the prize fund

We have rollovers

II's standpoint was that

I told you already in the "I Ching" thread. In the UK national lottery before they introduced the "lucky dip", one could indeed pick certain combinations of numbers so that ones average payout will be greater than 100%. I also pointed out that you will be unlikely in practise to actually benefit from that. You need to start getting 4 or more numbers for the strategy to start paying off. I've only ever won £10 once (for 3 numbers).


My contention was that this type of thing only occurs when there have been multiple rollovers and even then very rarely. When this happens the number of people playing increases considerably and so we may have, say 30,000,000 entries for a £14,000,000 jackpot. THe chances of splitting the pot are very high.

II pointed out that his numbers were VERY unusual and so he would be unlikely to have to share the prize.

I pointed out that only 7 times in hundreds of draws has the payout exceeded £14,000,000 for each recipient/syndicate (only an empirical measure, I understand)

http://host.randi.org/vbulletin/showthread.php?s=&threadid=33930&highlight=national+and+lottery


Not very interesting


What I was trying to point out earlier in this thread is that Ian tends to "trust to gut" when it comes to this kind of thing rather than trying to do a rigorous proof.

Sometimes my gut is wrong but Ian's gut "is always right"

[scribble]

Originally posted by The Don
Sometimes my gut is wrong but Ian's gut "is always right"


Where did I hear this?

"Once we disregarded all contrary evidence, proving our hypothesis was simple."

[ceptimus]

Ian,

You said you don't understand math, and want to use the English language. This is easy as the problem you ask is directly equivalent to this one:

Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.

Now, as we have repeatedly told you, but you refuse to acknowledge, the answer is No.

The flaw in your argument is that such a book could consist, for example, entirely of the letter 'A' repeated indefinitely - that is just as likely as the book containing any other sequence. The book could just as soon consist of copies of Moby Dick, repeated again and again, or copies of Moby Dick with slight spelling and punctuation errors. If the word you were searching for was "microprocessor", then you would never find it, as that word is not part of the novel "Moby Dick".

Now I doubt that you are too thick to understand this, but I'm pretty sure you won't be gracious enough to admit your error and apologise to everyone for your repeated insults.

[Lothian]

Ian, you have the gamblers fallacy. That ball could land on black forever.

[Interesting Ian]

Originally posted by scribble
It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

{sighs}

Knew this would be a waste of time. You're simply too stupid to understand.

Look, if it is probabilistically possible that the requisite sub-string will never show, then what is this probability??

Do you understand you must answer this question??

Whatever probability you name, unless it is zero, or unlimitedly close to zero, I can add further numbers showing your figure is wrong. At this stage I really don't think I can say anymore.

[Interesting Ian]

Originally posted by Cecil
I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

I understand the humour, but it's not comparable because gnome is not communicating in English where as I am.

[Interesting Ian]

Originally posted by Zep
Would it be fair to say that Ian has confused the idea that a given digit MUST occur in a string of digits of arbitrary length, as opposed to the PROBABILITY that it will occur in that same string?

No it wouldn't. I'm talking about probability. I repeat, if people are wrong give me the probability that it will never occur.

It's that simple.

[Interesting Ian]

Originally posted by Cecil
ExAyAz ((UnderstandingOf(y,z) > UnderstandingOf(x,z)) /\ UnderstandingOf(x,x) = 0)

(Pretend the E is backwards and the As are upside down)

Proof? Look at the third post in this thread.

Right, so you've now changed your mind and are wholly in agreement with everyone else?

[Kullervo]

Originally posted by ceptimus
Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.May I suggest a short story by Borges? The Library of Babel (http://www.analitica.com/bitblioteca/jjborges/library_babel.asp)

[CFLarsen]

Originally posted by The Don
You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0.

He did?? You're kidding, right?

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.

[Lothian]

Originally posted by Interesting Ian


{sighs}

Knew this would be a waste of time. You're simply too stupid to understand.

Look, if it is probabilistically possible that the requisite sub-string will never show, then what is this probability??

Do you understand you must answer this question??

Whatever probability you name, unless it is zero, or unlimitedly close to zero, I can add further numbers showing your figure is wrong. At this stage I really don't think I can say anymore. Perhaps you are right, You with almost no mathematical education at all has a unique solution. This solution is one that no one else agrees with.

The mistake you have make is that you forgot to class yourself along side the other famous people whose groundbreaking theories were originally laughed at.

Incidentally Lucianarchy has a groundbreaking probability theory as well, Perhaps you could discuss it with her next time you are at troll club.

[Interesting Ian]

Originally posted by The Don
Once again Ian, you have demonstrated a lack of understanding of (what used to be called 'O' level) mathematics. What you have said would SEEM to be intuitively true, but unfortunately it isn't.

You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0.



The lottery issue was one where it was very clear I was correct. It wasn't a mathematical problem as such. It should be very very clear that the numbers chosen affect the payout rate. I showed you and others the stats proving my point for christ sake man! And yes, in the past, before the introduction of the lucky dip and the Wednesday draw, and where there was a rollover, then indeed it was very likely that, by choosing appropriate numbers the payout rate would be over 100%.

[Interesting Ian]

Originally posted by T'ai Chi


Just to clarify since this changes the problem mathematically somewhat, are you interested in the total number of times '5' occurs in the sequence, or just the first time a '5' occurs? [/B]

Just the first time. In an unlimited search (adding on of numbers) what is the probability that 5 will never occur.

[LuxFerum]

I read this at least 3 times, and I think II is correct.

We have
S1=[a₁,a₂,a₃.....a_n]
And
S2=
with n>m


Originally posted by Interesting Ian
The question we're seeking to answer is whether it is probabilistically [b]possible whether the requisite number, ie "5", will never occur in the sequence, no longer how long we make it.

Or if S2∈S1 when n→ ∞

The probalility of S2 is not the first one of the (n-m+1) possible strings in S2 is:

1-(1/10)*(1/10)*(1/10).... = 1-1/10^m

The probalility of S2 is not one of the (n-m+1) possible strings is:

=(1-1/10^m)^(n-m+1)

when n→ ∞

=0


I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

[ceptimus]

Originally posted by LuxFerum
I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random. A book with just As is just as likely as any other book. Your argument is like the one people use when they say the lottery result: 1, 2, 3, 4, 5, 6 is less likely than a "random" sequence.

I admit that the probability of a random book consisting of nothing but As is vanishingly small, but that is not the same as saying it is impossible. A random book is just as likely to contain the works of Shakespeare, Dickens and so on - the probability of that is also vanishingly low but again not impossible.

[LuxFerum]

Another thing

How many times will a finite string appears in a infinite random string, if the chance of that string appears is different from zero?

I say that will appears a infinite numbers of times, therefore it will appear in a finite sub-set of the original infinite random string.

[The Don]

Originally posted by LuxFerum
Another thing

How many times will a finite string appears in a infinite random string, if the chance of that string appears is different from zero?

I say that will appears a infinite numbers of times, therefore it will appear in a finite sub-set of the original infinite random string.

I agree that in my opinion it will appear an infinite number of times.

I disagree with your second statement if I understand it, infinity divided by infinity is still infinity I think....

[LuxFerum]

Originally posted by ceptimus
A book with just As is just as likely as any other book. Your argument is like the one people use when they say the lottery result: 1, 2, 3, 4, 5, 6 is less likely than a "random" sequence.

I admit that the probability of a random book consisting of nothing but As is vanishingly small, but that is not the same as saying it is impossible. A random book is just as likely to contain the works of Shakespeare, Dickens and so on - the probability of that is also vanishingly low but again not impossible.
humm I see, the chance of a random infinite book consisting of A is 1/n whit n→ ∞, but so is the chance of any other sequence.
The only problem is that the "a" book is predictable, and we will not be able to tell the difference from an not random only "a" book. And if we extend the first book to infinity, they should stop showing only "a", because if it didnt, then it would certanly not be random.
For that reason, I don't think that that book should be viewed as random.

[angard]

I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.


An infinite number of really small persons sit in a room (large room)and toss a coin each, repeating this forever. (Heads or tails.) If someone gets tails he/she must leave the room. How many are there in the room after a really long time? (I can't say if I have the right answer myself, only what I think.)

[LuxFerum]

Originally posted by The Don


I agree that in my opinion it will appear an infinite number of times.

I disagree with your second statement if I understand it, infinity divided by infinity is still infinity I think....
Infinity/infinity in undeterminaded, If Im not mistaken.


Just make that finite sub-set the string that you are looking for, it is there, and it is finite.

[The Don]

Originally posted by angard


This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.


An infinite number of really small persons sit in a room (large room)and toss a coin each, repeating this forever. (Heads or tails.) If someone gets tails he/she must leave the room. How many are there in the room after a really long time? (I can't say if I have the right answer myself, only what I think.)

In my opinion:


The answer is that there will always be an infinite number of people inside the room.

There will be a finite number of people outside the room.

Infinity - finite number = infinity

[LuxFerum]

Originally posted by angard
Why? I thought all posssible outcomes or "strings" would be equally possible.
And it is, what I think is that infinity have a infinite numbers of infinite sub-sets.

[ceptimus]

Lux, Ian isn't talking about an infinite book. That is the whole point.

Now, we all agree that the opening of a random book is likely to be unintelligible, maybe something like this:

LKjhdklsjhkjyh duy8uJygfdh8YI gjhg98Y


But which of these exact sequences (for the first 40 characters, say) is the more likely?

"LKjhdklsjhkjyh duy8uJygfdh8YI gjhg98Y"
"It was the best of times, it was the blurst of times."
"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

I think you would agree they are all equally likely.

Now if the book is limited to upper and lower case letters, spaces and a few punctuation characters, say 60 characters in all, the probability that the first character is an A is: 1/60. The probability that the first two characters are both A is:
(1/60)². If the book is n characters long, the probability that consists of nothing but As is: (1/60)ⁿ

Unless maths has changed since I was at university, this is not zero, for any value of n, and it follows that Ian is wrong, and must apologise.

[edited for spelling and formatting]

[Interesting Ian]

Originally posted by epepke


I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

Psychologically people pick numbers spread out because they feel they are more random. There is also a propensity for people to choose numbers representing their birth dates. Therefore it seems likely to me that the payout rate will be greater if people pick numbers from 32-49, and also pick numbers clustered together. Not only does this make it more likely that you will not share the jackpot, but it also substantially increases the prize money for the smaller prizes.

But everybody was insisting I was wrong on that thread as well. And it's happened numerous times in the past where I've been the only one holding onto a position with everyone else disagreeing with me, and I was absolutely sure that I was correct.

So the very fact that everyone disagrees with me doesn't impress me. I mean it doesn't overcome the apparent logical inconsistency I see at the heart of this puzzle. But I emphasis I don't know anything about maths and, as I admitted in the other thread, I find the concept of infinity to be very obscure.

Now I've read a few of your posts around this board, and you seem to be a very intelligent guy, who's also clearly familiar with maths, and whom I don't feel would simply automatically take sides against me.

So I ask you

Are you absolutely sure that I'm incorrect??

I guess if you say I am, and my former allies are now opposed to my position (as Loki seems to suggest) it will be sensible to suppose I'm somehow wrong on this one issue.

I doubt if I'll ever understand how I am wrong though :(

What we have here is that p > 0 but that for anything above 0 we can always reduce by adding more numbers. I really don't understand how the probability is not unlimitedly close to 0 and hence 0.

Oh well

[Martin]

Originally posted by ceptimus

"It was the best of times, it was the blurst of times."You stupid monkey!

[Interesting Ian]

Originally posted by ceptimus
Ian,

You said you don't understand math, and want to use the English language. This is easy as the problem you ask is directly equivalent to this one:

[b]Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.

Now, as we have repeatedly told you, but you refuse to acknowledge, the answer is No.

The flaw in your argument is that such a book could consist, for example, entirely of the letter 'A' repeated indefinitely -



Yes, this is what everyone is claiming. One can get "A"s indefinitely. We will get "A"s forevermore, no matter how long we search. Nope, I don't understand how the probability is greater than 0 :) The problem is, is that people are simply using arguments that actually persuaded me, until I felt I was wrong about a year ago! LOL

[angard]

The answer is that there will always be an infinite number of people inside the room.

There will be a finite number of people outside the room.

Infinity - finite number = infinity


Just as I think. Not that it has much to do with the original problem but I thought of it when I read the other thread and found it amusing. Lots of people throwing only heads with a fair coin. :)

[Interesting Ian]

Originally posted by CFLarsen


He did?? You're kidding, right?

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.

Claus,

Go to the thread and read my arguments. When everyone expressed disbelief I even looked up the stats which confirmed my hypothesis that payout rates are much greater when picking numbers clustered together.

[LuxFerum]

Originally posted by ceptimus
Lux, Ian isn't talking about an infinite book. That is the whole point.
I think he is:
[First of all it should be made clear that infinitely close to 0, or unlimitedly close to 0 is exactly 0. I do not believe anyone does, or could deny this.....
..What is this limit? ...
..Either it reaches a limit which must be zero...
...unlimitedly close to zero,.....

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong.

[Interesting Ian]

Originally posted by Lothian
[B]Perhaps you are right, You with almost no mathematical education at all has a unique solution. This solution is one that no one else agrees with.



Well, other people were agreeing with me or apparently were agreeing with me. Dunno if they've changed their minds



The mistake you have make is that you forgot to class yourself along side the other famous people whose groundbreaking theories were originally laughed at.



I'd be more interested in you explaining how a probability can be greater than 0, and yet not be able to be reduced.

I feel a tad skeptical that everyone understands this apart from me. Go on, prove you understand.

[ceptimus]

Originally posted by LuxFerum

I think he is:

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong. From Ian's opening post in the previous thread:

"If the string is unlimitedly long (albeit not infinite), any given sub-string must occur."

Now he has ruled out infinite, but tried to foist on us this "unlimitedly long" thing. He won't say what that means, but he HAS SAID it is not infinite.

[wollery]

We've explained this several times and even given examples, but since Boring Ian seems to have no capacity to learn I'll try bashing it into his head.

PROBABILITY ZERO DOES NOT MEAN THAT SOMETHING CAN'T HAPPEN!!!

Ian was shown an example of this.

Use a random number selector to pick any real number of any amount of digits between 0 and 1.
What is the probability that the random number selector picks any particular number (say 0.5)?
Since there are an infinity of numbers between 0 and 1 and each is equally likely to be picked the probability for any single number is P=1/infinity which is infinitesimal, or 0.
However, since we are picking a number between 0 and 1 it follows that one of these numbers will be picked.
Now this number had a formal probability of being picked of 0. But it was picked.
Therefore we must conclude that having a probability of 0 does not mean that an event cannot happen!

This is the problem with Ians' proof. He is right that the probability of not finding his specified string approaches zero as the string length approaches infinity. What he has failed to connect to this is that this doesn't mean that it can't happen, just that it is incredibly unlikely.

Of course it may be the case that Ian has indeed made this connection, but is just too egotistical and arrogant to admit that he could possibly be wrong. But I doubt it, I think he's just a stupid prat with an overblown sense of his own intelligence and importance.

PS I think it also important to note that even having an infinite string does not guarantee that you will find your desired substring.

[Interesting Ian]

Originally posted by LuxFerum
I read this at least 3 times, and I think II is correct.

We have
S1=[a₁,a₂,a₃.....a_n]
And
S2=[b₁,b₂,b₃....b_m]
with n>m



Or if S2∈S1 when n→ ∞

The probalility of S2 is not the first one of the (n-m+1) possible strings in S2 is:

1-(1/10)*(1/10)*(1/10).... = 1-1/10^m

The probalility of S2 is not one of the (n-m+1) possible strings is:

=(1-1/10^m)^(n-m+1)

when n→ ∞

=0


I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

Yes, this was my thinking. I'm baffled that people are so completely sure I'm incorrect :confused:

Hmmm . .how do you do that infinity symbol?? Does n followed by that arrow thing mean that n approaches infinity but doesn't . .er . . "reach it"?

Your position seems to be the same as mine.

[69dodge]

Originally posted by epepke
So, in your paradox, you're using probability. That's fine. It's usually defined over the real interval [0..1], but it's also possible to define consistent probabilistic systems over all real numbers. Or over the complex numbers or some range thereof. (That's where it ends for probability; the rules stop working beyond that.)Complex probabilities? Can you say a bit more about that?

[Lothian]

Originally posted by Interesting Ian

I really don't understand how the probability is not unlimitedly close to 0 and hence 0.

Oh well Ian, What you are saying, probability aside, is can a number be so small that it is effectively 0.

The answer is yes. It can be so small that it is ‘effectively zero’ but it is not zero.

Zero looks like this 0

Efecttively zero looks like this 0.00000000000…………………………0001.

Mathematically they give practically identical results but there are nevertheless different numbers. Don’t try to be clever think like a 5 years old. Do the two numbers above look the same ?

[The Don]

Originally posted by Interesting Ian


Yes, this is what everyone is claiming. One can get "A"s indefinitely. We will get "A"s forevermore, no matter how long we search. Nope, I don't understand how the probability is greater than 0 :) The problem is, is that people are simply using arguments that actually persuaded me, until I felt I was wrong about a year ago! LOL

Is there anything anyone can do to attempt to persuade you to think differently ? What kind of demonstration would be required ?

[LuxFerum]

Originally posted by Interesting Ian
Yes, this was my thinking. I'm baffled that people are so completely sure I'm incorrect :confused:
That is only correct if you use an infinite string.

Originally posted by Interesting Ian

Hmmm . .how do you do that infinity symbol??

just put &# 8734 without the space before the number.

Originally posted by Interesting Ian

Does n followed by that arrow thing mean that n approaches infinity but doesn't . .er . . "reach it"?

That means that when n approaches infinite the probality approaches zero.

The only problem that I see in your reasoning is that you don't assume the string to be infinite, you assume that it is "unlimitedly long", but that is infinite. Without that, you can make the probability be as close to zero as you want, but not infinitely close, because you would only get that with an infinite string.

[CFLarsen]

Originally posted by Interesting Ian
Go to the thread and read my arguments. When everyone expressed disbelief I even looked up the stats which confirmed my hypothesis that payout rates are much greater when picking numbers clustered together.

Just a quick question: Do you really think that a probability can be greater than 1?

[Lothian]

Ian, for the lottery.

If you pick numbers that no one else ever picks you are guaranteed that you will not share the prize. It does not however mean that you are guaranteed to win or that your numbers have an average payout above 1.

I think I understand your argument , illustrated by this simple example.

10 people play. 9 always pick number 0 you always pick 9.

Stake £1 each total £10. £5 to good causes £5 to winnings. Rollovers apply

You will win on average over time as often a everyone else that means that your average return will be 5/2 or £2.5 for every £1 staked.

Now if 10 play but 4 always pick 0; 5 always pick 1 and you always pick 9 you will be the winner 1/3 of the time and your weekly return will be £5/3 for a £1 stake.

If 2 always pick 0; 2 always pick 1; 2 always pick 2; 3 always pick 3 and you always pick 9 then you will win 1/5 of the time and therefore you expected earnings are 5/5 or £1 for a £1 stake. You break even.

It follows that the key factors are the amount of the stake that goes back to prizes and the number of different combinations picked.

Assuming that you are the only person who ever picks your numbers then as long as the number of combinations selected is as a percentage less than the percentage of stake money returned as prizes then you could over time theoretically make a profit.

However in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

[Interesting Ian]

Originally posted by angard


This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.



Because the probability unlimitedly approaches 0. How can it not unlimitedly approach zero?? :confused:

I mean look at your example. The prob of getting all heads goes from 1/4 to 1/8. And the probability gets smaller and smaller without limit. So how come we don't get an unlimited small probability? :confused:

[The Don]

I think I understand where II is coming from. I don't agree but I think I DO understand.

It is agreed that any substring will be found in a string of infinite length.

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!!

[The Don]

Originally posted by Lothian
in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

Or empirically, to have had a payout proportion of > 100%, the value paid to each winner would have to exceed £14m (ish)

this would cover:
Jackpot 14m, one winner
Jackpot 28m, two winners etc

In all the time the lottery has been running on only 7 occasions has the payout per winner/syndicate been greater than 1/odds against.

[Interesting Ian]

Originally posted by LuxFerum

I think he is:

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong.

Ah right. No I don't understand what infinitely long means. I was referring to a string unlimitedly long ie no limits to how long it is before getting required results.

Now everyone seems to understand this apart from me:

But I'm quite unable to understand how a probability can be greater than 0, and yet not be able to be reduced. :confused:

[wollery]

Originally posted by The Don
I think I understand where II is coming from. I don't agree but I think I DO understand.I think most of us understand where Ian is coming from.:D

It is agreed that any substring will be found in a string of infinite length.No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!! this only works if you can guarantee that said substring will be in any infinite string, but as pointed out above this is not the case.

[Interesting Ian]

Originally posted by ceptimus
From Ian's opening post in the previous thread:

"If the string is unlimitedly long (albeit not infinite), any given sub-string must occur."

Now he has ruled out infinite, but tried to foist on us this "unlimitedly long" thing. He won't say what that means, but he HAS SAID it is not infinite.

I'm sick of saying what it means! :mad: It means a search without limits! So the probability MUST be driven unlimitedly close to zero.

But the search will not be an infinite one. Just unlimited.

[angard]

I mean look at your example. The prob of getting all heads goes from 1/4 to 1/8. And the probability gets smaller and smaller without limit. So how come we don't get an unlimited small probability?

Ofcourse I agree it gets smaller. That wasn't why I posted that though. I do not agree that the different outcomes are given different possibilites, that is: As the tossing goes on and on, why can't the possibility that is all HHHHHHHHHHH... be the one that is tossed and the given sub-string that you look for is T. I mean ist just as probable for that string to occur as some other string HTHHHTTTTTT... or? I dont see why it matters that the prob gets smaller though if its evenly distributed over possible outcomes.

I say you won't find your tails, because of all the heads.

I could be way of here, but this is what I think.

[Lothian]

Originally posted by Interesting Ian


I'm sick of saying what it means! :mad: It means a search without limits! So the probability MUST be driven unlimitedly close to zero.

But the search will not be an infinite one. Just unlimited. Chambers 20C dictionary.

Infinite: without end or limit

[Interesting Ian]

Originally posted by wollery
We've explained this several times and even given examples, but since Boring Ian seems to have no capacity to learn I'll try bashing it into his head.

PROBABILITY ZERO DOES NOT MEAN THAT SOMETHING CAN'T HAPPEN!!!

Ian was shown an example of this.

Use a random number selector to pick any real number of any amount of digits between 0 and 1.
What is the probability that the random number selector picks any particular number (say 0.5)?
Since there are an infinity of numbers between 0 and 1 and each is equally likely to be picked the probability for any single number is P=1/infinity which is infinitesimal, or 0.
However, since we are picking a number between 0 and 1 it follows that one of these numbers will be picked.
Now this number had a formal probability of being picked of 0. But it was picked.
Therefore we must conclude that having a probability of 0 does not mean that an event cannot happen!

This is the problem with Ians' proof. He is right that the probability of not finding his specified string approaches zero as the string length approaches infinity. What he has failed to connect to this is that this doesn't mean that it can't happen, just that it is incredibly unlikely.

Of course it may be the case that Ian has indeed made this connection, but is just too egotistical and arrogant to admit that he could possibly be wrong. But I doubt it, I think he's just a stupid prat with an overblown sense of his own intelligence and importance.

PS I think it also important to note that even having an infinite string does not guarantee that you will find your desired substring.

And what Wollery says is completely irrelevant as I am talking exclusively about probability.

I've already stated to him I perfectly understand his point. But he doesn't get it. He also doesn't get that his objection to my reasoning is different from everyone elses who are exclusively talking about probabilities, not logical possibilities.

PS And how the hell can you approach infinity?? :confused: Is this the same as infinity?? Or do people mean by it my unlimited?? :confused:

[The Don]

Originally posted by Interesting Ian

But the search will not be an infinite one. Just unlimited.

And by unlimited, you mean that you'll keep giong no matter how long it takes but that you'll stop once you find it ?

[Interesting Ian]

Originally posted by Lothian
Ian, What you are saying, probability aside, is can a number be so small that it is effectively 0.

The answer is yes. It can be so small that it is ‘effectively zero’ but it is not zero.

Zero looks like this 0

Efecttively zero looks like this 0.00000000000…………………………0001.

Mathematically they give practically identical results but there are nevertheless different numbers. Don’t try to be clever think like a 5 years old. Do the two numbers above look the same ?

Well, you know, my opponents keep contradicting each other LOL

Yes, I'm in agreement that I'm wrong if you're correct. I don't think you are correct though :) I would say 1 and 0.9 recurring are the same number. Wouldn't you?

[Interesting Ian]

Originally posted by The Don


Is there anything anyone can do to attempt to persuade you to think differently ? What kind of demonstration would be required ?

Yes, answer the conundrum of how P > 0 yet P can always be reduced, and yet P doesn't get unlimited close to 0 :)

[wollery]

Originally posted by Interesting Ian
And what Wollery says is completely irrelevant as I am talking exclusively about probability.

I've already stated to him I perfectly understand his point. But he doesn't get it. He also doesn't get that his objection to my reasoning is different from everyone elses who are exclusively talking about probabilities, not logical possibilities.And as I've said before, to talk about probability you must talk about all possibilities. That's what probability is

PS And how the hell can you approach infinity?? :confused: Is this the same as infinity?? Or do people mean by it my unlimited?? :confused: You approach infinity carefully and without sudden movements so as not to upset it.:D

Seriously though, approaching infinity means an incredibly large number which is not infinite, so yes, I believe that is what you mean by unlimited.

[Interesting Ian]

Originally posted by LuxFerum

That is only correct if you use an infinite string.


just put &# 8734 without the space before the number.


That means that when n approaches infinite the probality approaches zero.

The only problem that I see in your reasoning is that you don't assume the string to be infinite, you assume that it is "unlimitedly long", but that is infinite. Without that, you can make the probability be as close to zero as you want, but not infinitely close, because you would only get that with an infinite string.

There was some confusion over this in the other thread. People were saying that the way I was using the term unlimited is the same as infinite. I didn't feel it was, but was then wavering in my argument. But then other people came on my side and vorticity said that unbounded is not the same as infinity; which is what I kinda thought.

[The Don]

Originally posted by Interesting Ian
I would say 1 and 0.9 recurring are the same number. Wouldn't you?

IMO you have to make the distinction between functional difference and definition difference.

Functionally they are (almost) always indistinquishable. Of course under certain circumstances 1 and 1,000,000 are functionally indistinguishable (in this case adding (in pounds) to government spending and the material effect this will have).

By definition however they are different

[The Don]

Originally posted by Interesting Ian


Yes, answer the conundrum of how P > 0 yet P can always be reduced, and yet P doesn't get unlimited close to 0 :)
Take any value of P however small

Half it


There you go :D

[Interesting Ian]

Originally posted by CFLarsen


Just a quick question: Do you really think that a probability can be greater than 1?

I'm pretty convinced with a rollover. Without a rollover? Very possibly.

Please be aware though that I'm talking about the UK lottery in its first 2 years of operation where there was only 1 draw a week, and crucially there was no "lucky dip". A lucky dip is what people tick to get a random selection of numbers.

Why the hell they had to introduce that I don't know. I stopped going on the lottery for 8 years as a result because obviously any prizes I win would be that much less.

I pick numbers like 11, 43,44,45,46.48

[Suggestologist]

Originally posted by scribble
It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

"infinitessimal" doesn't mean zero? You should tell that to the people who think .99999... = 1.

Isn't it enough to show a counterexample to prove that the probability of no 5 is not zero? .999... is a counterexample.

[The Don]

Originally posted by CFLarsen


Just a quick question: Do you really think that a probability can be greater than 1?

Watch out Ian, Claus is trying to "trick" you with your own words. A certain loseness has allowed probability to be used in lace of "average return"

In a two horse race, if both horses are 2-1 (your bookie is an idiot) your average return would be > 100 % if
- the horses were equally likely to win and/or
- you bet equally on both of them
(e.g. you place a £1 bet on each horse and you'll always get £3 back - against your £2 stake)

Your probability of doing so will never exceed 1

[CurtC]

Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

[Interesting Ian]

Originally posted by Lothian
Ian, for the lottery.

If you pick numbers that no one else ever picks you are guaranteed that you will not share the prize. It does not however mean that you are guaranteed to win or that your numbers have an average payout above 1.

I think I understand your argument , illustrated by this simple example.

10 people play. 9 always pick number 0 you always pick 9.

Stake £1 each total £10. £5 to good causes £5 to winnings. Rollovers apply

You will win on average over time as often a everyone else that means that your average return will be 5/2 or £2.5 for every £1 staked.

Now if 10 play but 4 always pick 0; 5 always pick 1 and you always pick 9 you will be the winner 1/3 of the time and your weekly return will be £5/3 for a £1 stake.

If 2 always pick 0; 2 always pick 1; 2 always pick 2; 3 always pick 3 and you always pick 9 then you will win 1/5 of the time and therefore you expected earnings are 5/5 or £1 for a £1 stake. You break even.

It follows that the key factors are the amount of the stake that goes back to prizes and the number of different combinations picked.

Assuming that you are the only person who ever picks your numbers then as long as the number of combinations selected is as a percentage less than the percentage of stake money returned as prizes then you could over time theoretically make a profit.

However in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

Remember we have the "lucky dip" now. The prizes awarded vary enormously. For example getting 4 numbers has been as low as £15, but as high as £200. Getting 5 numbers plus bonus from about £7,500 to about £1,300,000.

Picking combinations of numbers that other people will be ill-disposed to pick is crucial.

[Interesting Ian]

Originally posted by The Don
I think I understand where II is coming from. I don't agree but I think I DO understand.

It is agreed that any substring will be found in a string of infinite length.

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!!

Hmmmm . . . yes . . .this seems to be another way of putting it. Have to think about this.

[LuxFerum]

Originally posted by wollery
No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!
I disagree. An infinite string contain all infinite sub-string.
infinity+infinity = infinity
You can simply add those infinite strings and it will be still a infinite string.

infinity+infinity+...... = infinity

[LuxFerum]

Originally posted by Interesting Ian
There was some confusion over this in the other thread. People were saying that the way I was using the term unlimited is the same as infinite. I didn't feel it was, but was then wavering in my argument. But then other people came on my side and vorticity said that unbounded is not the same as infinity; which is what I kinda thought.
from http://thesaurus.reference.com/search?q=unbounded

Synonyms: great, illimitable, immeasurable, immense, incalculable, indefinite, inexhaustible, infinite

It is. Specialy in the way you use it.

You can only get that chance to zero if you make the string infinite. Otherwise it is bigger than zero.

[Interesting Ian]

Originally posted by The Don


Or empirically, to have had a payout proportion of > 100%, the value paid to each winner would have to exceed £14m (ish)

this would cover:
Jackpot 14m, one winner
Jackpot 28m, two winners etc

In all the time the lottery has been running on only 7 occasions has the payout per winner/syndicate been greater than 1/odds against.

Bear in mind there is more than the jackpot to win!

Look, before the lucky dip was introduced I noticed that when the results were of such a nature that the balls tended to be clustered together, either no-one won the jackpot, or one person did. It was relatively infrequently 2 or more. *And* the jackpot tended to be higher on those occasions, tending to be about £12 million rather than the normal £9 or £10 million.

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip.

[The Don]

Originally posted by wollery
No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!


Of course, I was entirely wrong. In an infinite set of infinitely long strings there will be an infinite number of strings which repeat "TheDonWasBeingAFrikkinIdiot" and infinite number of times.

Thanks for putting me straight

[CFLarsen]

Originally posted by Interesting Ian
I'm pretty convinced with a rollover. Without a rollover? Very possibly.

In your own words, what does a probability of 1 mean?

[Interesting Ian]

Originally posted by The Don


And by unlimited, you mean that you'll keep giong no matter how long it takes but that you'll stop once you find it ?

Yes. I think what you said is another way of putting it.

[Interesting Ian]

Originally posted by The Don

Take any value of P however small

Half it


There you go :D

Yes, well maybe we've got this sorted out. Unlimitedly close to zero doesn't equal zero. If this is so, I am wrong! But people such as "Skeptic" were saying that unlimitedly close to zero *is* zero in the other thread.

[69dodge]

Originally posted by Suggestologist
Isn't it enough to show a counterexample to prove that the probability of no 5 is not zero? .999... is a counterexample.I do not understand this.

If I claim that "such-and-such is true in all cases", and you show me a case where such-and-such isn't true, you've provided a counterexample to my claim and thus disproved it.

We're trying to determine the probability of an event here. There are no claims that anything is true in all cases. How does the idea of a counterexample even apply?

[wollery]

Originally posted by LuxFerum

I disagree. An infinite string contain all infinite sub-string.
infinity+infinity = infinity
You can simply add those infinite strings and it will be still a infinite string.

infinity+infinity+...... = infinity Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(

Of course it's possible, and that string will not contain any other substrings. You can of course specify an infinite string which contains all possible finite and infinite substrings, but that's a different infinity.

As I said, infinity is a very complex and counterintuitive thing.

[Suggestologist]

Originally posted by 69dodge
I do not understand this.

If I claim that "such-and-such is true in all cases", and you show me a case where such-and-such isn't true, you've provided a counterexample to my claim and thus disproved it.

We're trying to determine the probability of an event here. There are no claims that anything is true in all cases. How does the idea of a counterexample even apply?

The way I've understood the question is that it hinges on having a probability of zero that a substring doesn't appear in a random string of arbitrary length. A probability of zero implies a statement about all cases; and thus should be vulnerable to a counterexample.

[Interesting Ian]

Originally posted by The Don
[B]

Watch out Ian, Claus is trying to "trick" you with your own words. A certain loseness has allowed probability to be used in lace of "average return"



Damn, think I've already responded to him LOL Dunno if I fell into the trap, can't remember.

[Interesting Ian]

Originally posted by CurtC
Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

Yes, this is what I'm saying. But people definitely don't seem to be agreeing with it! :eek:

[Interesting Ian]

Originally posted by LuxFerum

from http://thesaurus.reference.com/search?q=unbounded


It is. Specialy in the way you use it.

You can only get that chance to zero if you make the string infinite. Otherwise it is bigger than zero.

Right, we definitely disagree :) I'm only "approaching infinity" ( I believe this is the same as my unlimited although the words taken literally are a flat out oxymoron!)

[The Don]

Originally posted by Interesting Ian


Bear in mind there is more than the jackpot to win!

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip.

Absolutely, I agree however....

If you win the jackpot, you don't get any of the other prizes. You don't, for example get jackpot plus the 5,4,3 ball wins.

W.r.t. the prize fund, only the jackpot amount is incremented when there's a rollover so that's the only element of the winnings which is proportionally improved as a result.

The payout on three numbers is £10, the odds 1 in 54that's a payback of something under 20%

The odds of matching 4 numbers are 1 in 1,032.40 the payout is around £100 a payback of 10%

The odds of matching 5 numbers are 1 in 54,200.84 the payout is less than £3000 a payback of around 5%

The odds of matching 5 numbers plus bonus ball are 1 in 2.3 million. the payout is around £100K, again 5% return

The payback for these is negligible. The only way to materially beat the odds is to score a solo jackpot of £13m+ (or share one of £26m etc.) and that's only been done seven (7) times

The advice you give is good however. If you are foolish enough to play the lottery pick high numbers (as you suggest). This will limit your losses.

[angard]

If I throw a bucket with an infinite number of coins up into the air, is it possible for all those coins to land heads up or no?

[LuxFerum]

Originally posted by wollery
Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(

If you add an infinite string of 1s with an infinite string of 2s, will they not be infinite anymore?

Originally posted by wollery
Of course it's possible, and that string will not contain any other substrings. You can of course specify an infinite string which contains all possible finite and infinite substrings, but that's a different infinity.

How can it be a different infinty? :confused:
Infinity is infinity.


Originally posted by wollery
As I said, infinity is a very complex and counterintuitive thing.
Yes, that is why I think it is possible for it to have another infinites strings in there.

[Wudang]

Ian, let me try an analogy. The probability is 0 at infinity, okay? So I stick you in a car with a 10-year old and start driving, me wearing earplugs, and tell the kid "We're going to infinity". At 1-minute intervals the kid asks "Are we there yet?". This is an unlimitedly-long journey (we keep driving until you surrender) but not infinite. It will feel like infinity but it will not BE infinity. :D

[The Don]

Originally posted by Interesting Ian
Dunno if I fell into the trap.

I heard the thud from here I'm afraid. Some of these words have very specific meanings

[Interesting Ian]

Originally posted by wollery
Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(



Yes, most definitely. This I'm absolutely sure of. It simply isn't possible to obtain. As I say you confuse logical possibility with possibility.

But we're talking about our Universe.

It is logically possible for you to walk around without a head with all your senses and cognitive faculties intact. But that is simply not interesting.

Zero probability means impossible (although not of course logically impossible, but this is of absolutely no relevance).

[Lothian]

Originally posted by Interesting Ian


Bear in mind there is more than the jackpot to win!

Look, before the lucky dip was introduced I noticed that when the results were of such a nature that the balls tended to be clustered together, either no-one won the jackpot, or one person did. It was relatively infrequently 2 or more. *And* the jackpot tended to be higher on those occasions, tending to be about £12 million rather than the normal £9 or £10 million.

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip. What you are thinking is correct but you need to be careful how you say it.

Presume that the name number play each week. Group payouts for each level 6 balls, 5 balls + bonus, 5 balls..& 4 balls will be similar each week. The group payout is split according to the number of winners. So if half the number of people win then the payout will be twice as much. It follows that to get more money you want to be one of few people with that number of balls.
It is true that people don’t tend to cluster their picks and pick low numbers. It follows that if you cluster high numbers AND WIN then you are more likely to be a 'solo' winner.

But the important thing to note is that the above assumes you win. By clustering high numbers you have exactly the same chance of winning as someone picking birthdays.

While it is true that over the long term the expected payout of someone picking a set of numbers that no-one else picked would be higher than someone whose set of numbers matched others. It is not true to say that the expected payout would be greater than the stake. In other words by picking high grouped numbers you may over a long period lose less but you will still lose (lucky dip or not).

The 12 million and 10 million jackpots purely relate to the numbers of players. If you watch the show the announcers tell you the jackpot before the draw. Surely you are not saying the size of the jackpot affects the balls drawn out !

[LuxFerum]

Originally posted by Interesting Ian
I'm only "approaching infinity"
If you are only approaching infinity, the probability only approach zero. And approaching zero is different from infinitely close to zero and it is different from zero.

[69dodge]

Originally posted by Suggestologist
The way I've understood the question is that it hinges on having a probability of zero that a substring doesn't appear in a random string of arbitrary length. A probability of zero implies a statement about all cases; and thus should be vulnerable to a counterexample.I still don't see how this might work. You'll show me an infinitely long string that doesn't contain the desired substring, and I'll say, "yes, very nice, but that infinitely long string has probability 0." Where have we gotten? And what does .999... have to do with it?

[iain]

Ian,

Given that by your own admission you do not fully understand the maths or the concepts involved here; and given that people who do have explained it many many times and so clearly that even I can understand both your and their arguments and see that they are right, why are you not willing to concede even the possibility that you may simply be wrong.

I understand that in R&P you hold your opinions and there is room in philosophy for people to hold genuinly irreconcilable views; but in mathematics there is right and there is wrong.

To not even admit the possibility that you might be mistaken must surely mark you out as someone at the most basic level of wisdom : not only do you not know, not only do you not know that you don't know, but even when faced with a large number of knowledgable people generously giving their time to explain carefully to you where you are going wrong, you refuse to even acknowledge the possibility that you don't know.

Might I suggest that you pay for a maths course (e.g. with the Open University). Then at least the person who you're refusing to learn from will be being paid to have you refuse to learn from him/her. It just seems fairer.

[diddidit]

Should the word "asymptote" be used somewhere in this discussion of probability moving towards zero as number of samples moves towards infinity? That was the first thing that popped into my head.

did

[Interesting Ian]

Originally posted by The Don


Absolutely, I agree however....

If you win the jackpot, you don't get any of the other prizes. You don't, for example get jackpot plus the 5,4,3 ball wins.



:cry: :cry: :cry:

Oh well, £12 million will do :)



W.r.t. the prize fund, only the jackpot amount is incremented when there's a rollover so that's the only element of the winnings which is proportionally improved as a result.



Yes, a pity isn't it.



The payout on three numbers is £10, the odds 1 in 54that's a payback of something under 20%

The odds of matching 4 numbers are 1 in 1,032.40 the payout is around £100 a payback of 10%



On average £65 soon after lottery was launched. But been as low as £15 and as high as at least £200.



The odds of matching 5 numbers are 1 in 54,200.84 the payout is less than £3000 a payback of around 5%

The odds of matching 5 numbers plus bonus ball are 1 in 2.3 million. the payout is around £100K, again 5% return



As low as £7500 and as high as £1.3 million.



The payback for these is negligible.



But remember if you pick appropriate numbers and get near the high end of the ranges I mentioned, they would no longer be so negligible.


The only way to materially beat the odds is to score a solo jackpot of £13m+ (or share one of £26m etc.) and that's only been done seven (7) times


But with the numbers I choose, maybe something like
12, 41, 42, 43, 44, 46, it's unlikely that similar highly clustered balls have ever been winning balls. And if such a sequence did come out, then prior to the lucky dip, I think it would be a very good chance that I would be the sole winner. Also remember that "unusual" numbers often don't match with anyones chosen balls, so it's a bit misleading to quote statistics on solo jackpot wins.



The advice you give is good however. If you are foolish enough to play the lottery pick high numbers (as you suggest). This will limit your losses.

Yes, I will lose now on average with the introduction of the lucky dip. I think prior to this though that it was unclear whether my average winning were less than 100%. AVERAGE that is, I think I only ever won £20 despite spending about £150 in the period (1994-1996). Then when the LD was introduced I stopped playing because it was no longer worth it.

But for the past 2 months I've been spending a £1 a week because you can now do it online and automatically get emailed about your winnings with the money going automatically into your account.

[Interesting Ian]

Originally posted by Wudang
Ian, let me try an analogy. The probability is 0 at infinity, okay? So I stick you in a car with a 10-year old and start driving, me wearing earplugs, and tell the kid "We're going to infinity". At 1-minute intervals the kid asks "Are we there yet?". This is an unlimitedly-long journey (we keep driving until you surrender) but not infinite. It will feel like infinity but it will not BE infinity. :D

That's right, we can only "approach infinity" and get unlimitedly close to zero probability in the process :)

[Interesting Ian]

Originally posted by The Don


I heard the thud from here I'm afraid. Some of these words have very specific meanings

Well done Claus! :D Such an immensely intelligent person being able to successfully lay a trap. :eek: :rolleyes:

[ceptimus]

Sigh.

Ian doesn't understand xeno's paradox.

Lux doesn't know about the different classes of infinity.

People have allowed Ian to divert back onto his Lottery topic, which makes an admission of defeat and an apology from him even more unlikely.

:(

Do the decent thing and apologise for once Ian. It's not that hard.

[LuxFerum]

Originally posted by Interesting Ian


That's right, we can only "approach infinity" and get unlimitedly close to zero probability in the process :)
No. you don't get unlimitedly close to zero.
It is proportional to what you increase.
If you increase 10 time the string, the probality will reduce in 1/10¹⁰

that is not unlimitedly.
The size of the string is attached to how close you get to zero.
you can't get unlimitedly close to zero without getting inlimitedly close to inifinity.

[The Don]

Originally posted by ceptimus
<sigh>
People have allowed Ian to divert back onto his Lottery topic, which makes an admission of defeat and an apology from him even more unlikely.


Don't blame Ian, that was my fault, I was trying to demonstrate how Ian "trusts his gut" and using that as an example

Sorry :(

[Interesting Ian]

Originally posted by Lothian
What you are thinking is correct but you need to be careful how you say it.

Presume that the name number play each week. Group payouts for each level 6 balls, 5 balls + bonus, 5 balls..& 4 balls will be similar each week. The group payout is split according to the number of winners. So if half the number of people win then the payout will be twice as much. It follows that to get more money you want to be one of few people with that number of balls.
It is true that people don’t tend to cluster their picks and pick low numbers. It follows that if you cluster high numbers AND WIN then you are more likely to be a 'solo' winner.

But the important thing to note is that the above assumes you win. By clustering high numbers you have exactly the same chance of winning as someone picking birthdays.

While it is true that over the long term the expected payout of someone picking a set of numbers that no-one else picked would be higher than someone whose set of numbers matched others. It is not true to say that the expected payout would be greater than the stake. In other words by picking high grouped numbers you may over a long period lose less but you will still lose (lucky dip or not).

The 12 million and 10 million jackpots purely relate to the numbers of players. If you watch the show the announcers tell you the jackpot before the draw. Surely you are not saying the size of the jackpot affects the balls drawn out !

I remember back in 1995/1996 that the jackpot total was higher with clustered balls then spread out balls yes. Not sure how they do it.

Yes, I am no more likely to win, it's just that if I *do* win (4 balls or more) I would (and indeed will) win more. I would say that prior to the LD that my average winnings might well have been over 100%. Or close to 100%. Of course it is highly unlikely that I will actually really benefit much from such average winnings! LOL In practise I never benefited at all in fact because I have never got 4 balls or more.

[Interesting Ian]

Originally posted by iain
Ian,

Given that by your own admission you do not fully understand the maths or the concepts involved here;



But I can understand a logical incoherency, which is what appears to be involved here. Why would one necessarily have to know all about maths in order to recognise a logical incoherency?

A probability above 0, but such a probability can always be made lower by adding further numbers.

So it seems that this must be unlimitedly close to zero. And indeed some people agree with me! But they say this isn't the same as 0.

Basically almost everyone disagrees with me, but a lot of them are doing so for differing reasons!

So which of my opponents are you agreeing with?

What is it about my reasoning which is fallacious?




and given that people who do have explained it many many times and so clearly that even I can understand both your and their arguments



But they disagree with me for different reasons! Which opponents do you agree with??


and see that they are right, why are you not willing to concede even the possibility that you may simply be wrong.


If you think that then you're not reading my posts.



I understand that in R&P you hold your opinions and there is room in philosophy for people to hold genuinly irreconcilable views; but in mathematics there is right and there is wrong.



So I am wrong? I am definitely wrong?? Care to explain why??


Might I suggest that you pay for a maths course (e.g. with the Open University). Then at least the person who you're refusing to learn from will be being paid to have you refuse to learn from him/her. It just seems fairer.

How will attending a maths course resolve the logical paradox?

[LuxFerum]

Originally posted by Interesting Ian
A probability above 0, but such a probability can always be made lower by adding further numbers.
Yes, but it only can be unlimitedly close to zero if you add unlimitedly close to infinite numbers.

Originally posted by Interesting Ian
So it seems that this must be unlimitedly close to zero. And indeed some people agree with me! But they say this isn't the same as 0.
It is the same as zero only when you have infinite numbers.

Originally posted by Interesting Ian
So I am wrong? I am definitely wrong?? Care to explain why??

Yes, yes, because you don't see that you need to be infinitly close to infinity to have the probability infinitly close to zero.

[Interesting Ian]

Originally posted by LuxFerum

Yes, but it only can be unlimitedly close to zero if you add unlimitedly close to infinite numbers.


It is the same as zero only when you have infinite numbers.


Yes, yes, because you don't see that you need to be infinitly close to infinity to have the probability infinitly close to zero.

Luxferum, it might be a good idea for you to look in the other thread. I go into a lot of detail there. Also, as far as I am able to understand, my position is identical to 69Dodge and vorticity in there who also talk about such issues. :)

[CFLarsen]

Originally posted by Interesting Ian
Well done Claus! :D Such an immensely intelligent person being able to successfully lay a trap. :eek: :rolleyes:

There's no "trap", Ian.

In your own words, what does a probability of 1 mean?

[iain]

Originally posted by Interesting Ian
But I can understand a logical incoherencyThe evidence would not seem to support this.

Basically almost everyone disagrees with me, but a lot of them are doing so for differing reasons!More like people are trying to explain the same thing to you in different ways, hoping that you'll understand at least one of them. No luck yet, sadly.


What is it about my reasoning which is fallacious?I believe this has been answered many times in this thread. If you haven't spotted those answers, I can't imagine my adding another would be of any benefit.


If you think that then you're not reading my posts.Sadly, I have, and I can never regain those lost minutes of my life.

So I am wrong? I am definitely wrong?? Care to explain why??Many others have already and you haven't understood their explanations. I see no reason to think I would fare any better.


How will attending a maths course resolve the logical paradox? Because it might help you to understand that it isn't really a paradox - it has a correct mathematical answer. You only see it as a paradox because you don't understand that answer.

[Interesting Ian]

Originally posted by iain
The evidence would not seem to support this.

More like people are trying to explain the same thing to you in different ways, hoping that you'll understand at least one of them. No luck yet, sadly.


I believe this has been answered many times in this thread. If you haven't spotted those answers, I can't imagine my adding another would be of any benefit.


Sadly, I have, and I can never regain those lost minutes of my life.

Many others have already and you haven't understood their explanations. I see no reason to think I would fare any better.


Because it might help you to understand that it isn't really a paradox - it has a correct mathematical answer. You only see it as a paradox because you don't understand that answer.

Damn, I shouldn't have started a new thread. But I was drunk last night :)

Anyway, I think the latest post I made on there might be illuminating. I'll paste in here.

Originally posted by slimshady2357
Originally posted by Interesting Ian
Edit to add: I mean it's a bit like there's an infinite number of positive integers, but they are all finite, so an unlimited search will get to them. [/B]
--------------------------------------------------------------------------------



Do you really believe that? That if I can write down one positive integer per second say (no matter the length, man, my fingers are fast), given an "unlimited" but finite amount of time I will write them all down??

I must be reading what you said incorrectly.....



I'm saying that for any of those infinite number of positive integers, an unlimited search will reach it (we don't need an infinite search).


But in the same way, even though each string is of finite length, there are an infinite amount of them. So there is no way your probability becomes 1 unless you are willing to say you are able to check each one of an infinite number of strings (Though each string is finite).


There are an infinite number of strings, but each is finite, so by comparable reasoning you can get to any specified one by an unlimited though not infinite search (that was the oringinal problem)


Now, 2 issues here.

First of all do you agree that it's comparable to the positive integers example?

Secondly, if you are, do you agree an unlimited search (rather than infinite) will suffice?

Interesting stuff this if only people won't so keen to try and show me up :)

[Sundog]

THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

[Cleopatra]

Originally posted by Sundog
THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

The reason I like your posts so much Sundog is because you are a genuine "political animal" ( this is the exact translation from the Ancient Greek term Aristotle first introduced to describe the tendancy humans have to live together). You can see and spot the politics everywhere!! :)

[Suggestologist]

Originally posted by 69dodge
I still don't see how this might work. You'll show me an infinitely long string that doesn't contain the desired substring, and I'll say, "yes, very nice, but that infinitely long string has probability 0."

How do you come to such a conclusion? You're not saying that infinitely long strings are impossible, and therefore do not exist, are you?

And as someone else has mentioned, there are an infinite number of infinite strings with the same counterexemplar property.

Where have we gotten? And what does .999... have to do with it?

Well, someone mentioned the fact that infinitessimals (as hyperreals) are greater than zero. A previous discussion about .999... = 1, had people saying the opposite.

[Sundog]

Originally posted by Cleopatra


The reason I like your posts so much Sundog is because you are a genuine "political animal" ( this is the exact translation from the Ancient Greek term Aristotle first introduced to describe the tendancy humans have to live together). You can see and spot the politics everywhere!! :)

Heh. I think I've just been slammed, ever-so-nicely. :D

And here I thought you liked me for my body.

[Paul C. Anagnostopoulos]

Ian said:
There are an infinite number of strings, but each is finite, so by comparable reasoning you can get to any specified one by an unlimited though not infinite search (that was the oringinal problem)
It was? I thought the original problem had you generating digits until you matched a target. If you have the set of all strings of digits, your target is in that set. You don't have to generate anything or search.

~~ Paul

[Interesting Ian]

Originally posted by Sundog
THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

I do not at all think that all opinions are created equal. And I agree that as a layman, I should definitely not be able to outargue people very familiar with mathematics on this issue. Yet I believe I have. To be fair both Vorticity and 69Dodge hel