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[thebruce]

if there's an infinite number, there's an equal chance of a sequence definitely occurring as there is with it not possibly occurring at all... it's like division by 0... hehe

well, not exactly like division by 0, but as strange a concept to grasp...

[Olorin]

[neon snake]

I was actually being relevant when I started this - as in, if you look at an infinite string, you'll always see what you are looking for at some point, so it's prudent to avoid wishful thinking!

thebruce - tentatively, and waiting to be proved wrong, I disagree. Over a long enough timeline, and barring removal of naughty number 3, all possible combinations must occur. Somewhere in my maths textbooks from a decade or so ago, I have the mathematical proof. I think.

[Olorin]

[SilentAvenger]

Assuming really each digit has an equal chance to appear, (say, not the infinite-digit number 2/3, which nothing but 6's), the chance of an exact string of digits with length N to appear, is 1/10^N.

This means that for a number with K digits, there is a 1/10^N chance for each substring of size N to be equal to the string we are trying to match, so, K-N+1 equalling the number of N sized substrings, there is chance of (K-N+1)/10^N to find a string of length N in a string of length K (actually, its slightly less, but in general this is it).

So, assuming K is infinite and N finite, this will come out as infinite, that means, you will find you string repeated infinite times, not only once

A common way to show this, is to picture a monkey on a typewriter, typing off stuff for all times. It is obvious (assuming he types letters randomly, and that the typwriter doesnt jam, as monkeys dont know how to fix jammed typewriters) that at one point he must type the full works of Shakespear, one after another, in alphabetical order.

*turns off mathmode*

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[thebruce]

[thebruce]

I'll also add that the chance of e being a non-repeating infinite number in essence also becomes a matter of approaching 0%... but it will never be 0, because that would require a finite number to calculate the bounds... in essence, we'll never know if e is an infinite non-repeating number, if it is in fact just that.

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if it were repeating it would be a rational number --- e is not only irrational but transcendental

see

http://www.math.rochester.edu/people/grads/micah/Trans.pdf

for proof

[darkblaze]

all these numbers make me think about phi (its my favorite number!) theres an article in the guardian about it too but that was almost 2 years ago..

[am520dj]

ow, math, numbers, getting headache...

[neon snake]

[Shish]

I'm bored. Have some cents.

o) Any infinite random number will contain all finite number series
o) Any infinite non-repeating number will contain all finite number series
o) It's possible to have a non-repeating infinite number with a pattern like 123112233111222333 which will never contain the sequence "13"
o) It's possible for a random number generator to come up with the above pattern
o) perhaps the first two statements work if we also specify that it must be a patternless, unpredictable random number? Eg you can predict that the number after 1 will not be 3, and for it to be patternelss and unpredictable you must be wrong at some time.

One thinks this boils down to infinite force vs infinite wall: for a number to be random it must be unpredictable, and yet a RNG can come up with any series of numbers, including one with a pattern that has no 13. Using the first two unprovable statements, however, we can argue that for it to be random and infinite, it must at some point contain 13:

The chance of getting a one then a three is 1/9 * 1/9; 1/81. Given infinite chances and you get inf/81, aka infinite chance of it happening.

So which wins? the "all numbers must appear at some point" or the "if you can successfully predict that it'll happen, it isn't random"? Or, like the infinite force, are we thinking outside all the boxes, including that of reality?

[thebruce]

I still choose to believe that if a chance ever approaches 100% (or 0%) but never reaches it, then you may as well throw the argument out the window... if there's never a definite chance a sequence will appear, then essentially, there's always a chance it won't appear, so as you march on towards infinity, there's always a chance it will never appear just as much as there's a chance it will appear... infinite chances aren't arguable, afaic

with a limit to the length of a random number, you can, and never will, know whether or not a sequence will appear or not. "Until you find the sequence" already assumes it will exist. If you never find it, it doesn't mean it will never appear, but it doesn't mean it will. So I agree, as soon as you say a sequence has a specific chance to appear, you claim to either know that the number is repeating (and have therefore uncovered the entire set of numbers) or know that it's not an infinite number - ie, you've reached the bounds in order to calculate a specific chance. An infinite number, by default has no bounds, therefore a chance can't be mathematically calculated... a theoretica chance could (whatever the term may be), but it's theoretical... like 'as x approaches 10' - for all intents and purposes, we know x will never pass 10 and it will pass all decimal values up to 10, but we know x will never actually be 10... making 10 the theoretical maximum of x, even though x will never be 10...

math & infinity is a strange thing

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