[hkhanna]

Isn't it a property of infinity? If pi goes on infinitely without repeating itself, every possible combination of numbers appears somewhere in pi.

It's sort of like the idea that if the universe is infinitely big and mass and energy are randomly distributed throughout the universe, then an exact copy of you on an exact copy of Earth is out there somewhere.

This property of infinity has always fascinated me, so I'm very curious for where the logical fallacy might be.

[n2d4]

Not necessarily. The number 1.01001000100001000001... never repeats itself, yet most other numbers can never be found in it.

A number that contains all other numbers infinitely many times (uniformly) would be called normal, but no one has managed to prove this for pi yet. In fact, no one even managed to prove that pi doesn't contain only 0s and 1s like the above after the X-th digit.

[andrewla]

More trivially, there are an infinite number of even numbers, and they do not repeat, yet they do not contain a single odd number.

[constantcrying]

>Isn't it a property of infinity? If pi goes on infinitely without repeating itself, every possible combination of numbers appears somewhere in pi.

No. Example: 0.1011011101111011111... does never repeat, yet there is no 2 in there, neither is there 00 in there.

[onion2k]

The fact you can't encode arbitrary data in a structured-but-irrational number doesn't mean you can't encode data in a 'random' irrational number.

The question is really 'Does every series of numbers of arbitrary finite length appear in pi?' I can't answer that because I'm not a mathematician, but I also can't dismiss it, because I'm not a mathematician. It sounds like a fair question to me.

[fragmede]

just index on the number of ones. Ex 0.10110 there are two ones in a row, so reference those two ones to be the number two. For 00, flip it and refer to the same pair of ones.

[dist-epoch]

Most physicists don't believe that infinity can actually exist in the universe.

Put another way, the program which searches those works of art in the digits of pi will never finish (for a sufficiently complex work of art). And if it never finishes, does it actually exist?

[constantcrying]

>Most physicists don't believe that infinity can actually exist in the universe.

Citation needed.

Believing in real numbers requires you to believe in far more than infinity. How many physicists reject real numbers?