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

I don't understand why people say that just because a pattern goes on forever, like the decimals of pi, it is guaranteed to contain every possible number (for instance: 4538263829292747938272616). I hear actual teachers and professionals say the often quoted idea that "pi in binary contains every program ever written" when I can't fathom why that would be true. Why does something being infinite automatically entail that it contains everything?

Other urls found in this thread:

en.wikipedia.org/wiki/Infinite_monkey_theorem
libraryofbabel.info
theguardian.com/books/2015/may/04/virtual-library-of-babel-makes-borgess-infinite-store-of-books-a-reality-almost
mathoverflow.net/questions/142194/pi-disjunctive-numbers-and-finite-sequences-of-given-length
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/
twitter.com/AnonBabble

If a sequence is infinite and is not repeating, by definition it contains all possible finite sequences

How do we know a sequence doesn't repeat

Also I guess what stops it from going on forever without ever containing a specific subsequence ? How do we KNOW

>Why does something being infinite automatically entail that it contains everything?
We just assume it does. Based on the assumption that if everything has a chance of happening, no matter how small a chance it is, given infinite time, it will happen.

Actual answer here: we don't know for sure we just think it does.

what about
110100100010000100000100000010000000...
?

And yeah I agree, it always infuriates me when people share stupid memes with shit like this every pi day, when you can find a counter example if you just think about it for 1 second. In fact this property of infinite sequences is called being "disjunctive", and at the moment it's not known whether the decimal expansion of pi is disjunctive or not.

Same thing with prime numbers. We don't know if they go on forever, they just might suddenly stop at one point. We don't have a proof yet. Get to it you lazy weaaboos and do some number crunching

I think the confusion is closely related to the "infinity=everything" fallacy, where people for some reason assume that if something is infinite that it must contain every possible thing. This is obviously total bullshit, as the set of all even numbers is infinite but it certainly doesn't contain any odd numbers.
Moreover there is a very sensible way to measure an infinite set's size called "cardinality" (look it up), and you can prove that even though the set of all natural numbers is infinite and has the same cardinality as the set of rational numbers, the seat of real numbers has greater cardinality. In fact, for ANY set it's power set (the set of all subsets) will always have strictly larger cardinality.

In fact, the collection of all cardinalities of all infinite sets is SO HUGE that it can't itself be a set.

I'm just going to assume you're a troll and move on.