I don't understand why people say that just because a pattern goes on forever, like the decimals of pi...

>Why does something being infinite automatically entail that it contains everything?
It doesn't. Your understanding and those you criticize are flawed.

Counterexample: 0.11111.....

okay...?

Because it's not necessarily true, see

Euclid proved that there are infinitely many primes well over 2000 years ago, and it's the first thing any math student learns about prime numbers. So when someone says there's definitely no proof of this extremely well-known fact then I assume that they know what they're talking about and are just being a piece of shit.

in binary though...

Yea no you're right, I have no idea what the fuck I was talking about. Last time I'm commenting right after fapping

even in binary that sequence doesn't contain all finite strings though...

That's because in binary it's not an infinite non-repeating decimal. I don't even know if that user meant for it to be a decimal, which would be completely retarded.

Um... it's an infinite non-repeating string, no matter what the base is. If you want it to be a "decimal" you could just put '0.' in front of it. I'm not sure I understand what your problem is exactly.

Let's say you have an infinite string of text showing integers from 1 to 6. If you throw a die and note the results, no matter how many times you threw it, as long as it's finite, your sequence of results will be in that string of text. Just very far in the string if the sequence is lengthy enough.

This is not true at all. Take the string in but replace the 0's with 2's so it satisfies your criterion; then any roll which isn't a 1 or a 2 will not be in this string.

wrong

Because it's a transcendent number, not a fraction.

Why are you in a science board?

God...irrational numbers dont go indefinitely.

If the sequence in question is the decimal expansion of a real number, then it suffices to know that it's irrational, i.e. you can't write it as a ratio of two integers. Although pi is transcendental, that's kind of overkill since the square root of 2 has non-repeating decimal expansion but is still algebraic (i.e. it can be plugged into a polynomial with rational coefficients to make a rational number, whereas pi cannot).

To see that any irrational number has a non-repeating decimal expansion, you could do the following Contradiction argument. Take an irrational number r and suppose it has an eventually-repeating decimal expansion; suppose that the sequence starts repeating with period p sometime before decimal place d, and let n=n_1...n_p be the string of the next p digits, considered as an integer. If we let r' be the part of r before the d-th decimal place, then r' is a rational number because its decimal expansion actually terminates. Then we can write

r-r'= n x10^{-d} + n x10^{-d-p} + n x10^{-d-2p} + n x10^{-d-3p} +...
= n x(10^{-d} + 10^{-d-p} + 10^{-d-2p} + 10^{-d-3p} +...)

(There are many subtleties in the fact that this infinite sum converges to a finite real number and that you can factor out the number n, but I assure you that in this particular case it does and you can.)

Now we can actually compute this infinite sum. Supposing that its value is s, then s satisfies the equation

s x10^{-p} = s - 10^{-d}
(just take the infinite sum expression for s and plug it in to check, and I have to assure you again that in this particular case this is a valid move)
Then s= 10^{p}/ ((10^p -1)x10^d), which is rational.

Therefore our irrational number r is a sum
r = r' + nxs
of rational numbers, which is a contradiction. Therefore our assumptions are contradicting each other, so we have to conclude that given any real number r it can't be both irrational and have a repeating decimal expansion.

its kinda like the monkeys and the type writer and shakespear. If it makes you that upset I think you have a problem

...

That's a probabilistic principle and doesn't apply to EVERY infinite string. It's a subtle issue about measure theory, but the point is that just because an event has probability 0 that doesn't mean it can't happen.

en.wikipedia.org/wiki/Infinite_monkey_theorem

Are constants evil?

"We've heard that a million monkeys
at a million keyboards could produce
the complete works of Shakespeare;
now, thanks to the Internet,
we know that it is not true."
– Robert Wilensky, UC Berkeley (1996)

These statements are false.

That's pretty cool bro, but we're talking about pi.

I would suggest that this statement is true IF pi is normal, i.e. the distribution of all decimals is equal. This is not yet known.

What you said about pi is the totally correct answer bro, but I was responding to a specific statement about dice rolls which had a similar kind of misconception about infinite sequences.

Because the digits of [math]\pi[/math] are approximately uniformly distributed.

i like that quote thanks mate

What are you, 15?

>2016
>almost everything creative is with the work of the internet
>wilensky has thumbs up his ass

It isn't infinite and it does repeat. We just haven't reach it. Because, if it was really infinite that means it contains a copy of itself.....and infinite number of copies of itself actually.

lol Which the original is untrue anyway since monkeys would have a predisposition to repeat things and not be completely random.

The same way that
libraryofbabel.info
has your post, word for word, before you'd even typed it.

not OP but why shouldn't it? The copies you are talking about wouldn't be exact copies, compare it to an array:

[1,4,5,2,53,66,4]

The 4 is a copy of the other 4, but since it's position in the array isn't the same it is not the same object

This also works for exact same copies of Arrays

[[1,2,3],,[42,5,9,8],[1,2,3]]

Same Array, different position

>everything exist infinite times
>but everything is unique due to it cosmological position

>libraryofbabel.info

That's pretty fucking cool.

theguardian.com/books/2015/may/04/virtual-library-of-babel-makes-borgess-infinite-store-of-books-a-reality-almost

>the moment you search your own date of death

>The copies you are talking about wouldn't be exact copies

Since it is infinite, it would be. Saying a random number is infinite and doesn't repeat is just bad general logic.

ok, if (you) say so :^)

it depends on if every program written ever is infinite or finite. If it is finite it is contained in the binary expansion if it's infinite it may or may not be.

There are a disturbing number of people in this thread who are speaking with a tone of certainty but have no fucking clue what they're talking about.

(i don't think you know how definitions work)
(this isn't an assumption that mathematicians make, because it's false)
(we do have a proof that primes go on forever)
(false, for example if you have an infinite string with only 1s and 2s)
(irrational numbers necessarily have infinite, non-repeating decimal expansions, see )
(only a probabilistic phenomenon, doesn't apply to every single sequence)
(wrong and wrong, for reasons I've already pointed out)
(there are WAY more numbers with non-repeating decimal expansions than those which repeat)

An infinite non-repeating sequence doesn't need to contain every possible finite string (a counter-example was given in ). A sequence with such a property is special, it's called "disjunctive." Not every infinite non-repeating sequence is disjunctive.

Here's a starting point for learning about the current state of knowledge on whether the decimal expansion of pi is disjunctive or not: mathoverflow.net/questions/142194/pi-disjunctive-numbers-and-finite-sequences-of-given-length
tl;dr we currently DON'T KNOW whether pi's decimal expansion contains every possible finite string or not.

Please, for the fucking love of god, please stop assuming that infinity=everything. Think about things before you leap to conclusions. Math isn't a wishy-washy intuitive subject: if you haven't proven something rigorously, you don't know shit.

sincerely,
- someone who actually studies math

google.de/search?q=does an infinite non-repeating sequence contain every finite string?&rlz=1C5CHFA_enDE504DE504&oq=does an infinite non-repeating sequence contain every finite string?&aqs=chrome..69i57.30332j0j8&sourceid=chrome&ie=UTF-8

math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations

askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/

quora.com/Do-the-digits-of-pi-contain-every-possible-combination-of-numbers-from-0-to-9

goodmath.org/blog/2014/05/22/infinite-and-non-repeating-does-not-mean-unstructured/

reddit.com/r/askscience/comments/1aytmw/if_pi_has_an_infinite_nonrecurring_amount_of/

pathofthebeagle.com/2013/04/07/does-pi-contain-the-universe/

scienceblogs.com/builtonfacts/2013/04/12/everything-in-pi-maybe/

whoa...
really makes you thin, huh...

Library of babel was designed for such a thing. Pi was not.

False.
0.101100111000111100001111100000... is transcendental number that has digits approximately uniformly distributed and it does not contain every string(eg. 1010)