Prove that said number isn’t pi.
Prove that said number isn’t pi.
It kind of does come across as pedantic – the real question is just that “Does pi contain all sequences”
But because of the way that it is phrased, in mathematics you do a lot of problems/phrasing proofs where you would be expected to follow along exactly in this pedantic manner
OK, fine. Imagine that in pi after the quadrillionth digit, all 1s are replaced with 9. It still holds
The question is
Since pi is infinite and non-repeating, would it mean…
Then the answer is mathematically, no. If X is infinite and non-repeating it doesn’t.
If a number is normal, infinite, and non-repeating, then yes.
To answer the real question “Does any finite sequence of non-repeating numbers appear somewhere in Pi?”
The answer depends on if Pi is normal or not, but not necessarily
Hmm, ok. Let me retry.
The digits of pi are not proven to be uniform or randomly distributed according to any pattern.
Pi could have a point where it stops having 9’s at all.
If that’s the case, it would not contain all sequences that contain the digit 9, and could not contain all sequences.
While we can’t look at all the digits of Pi, we could consider that the uniform behavior of the digits in pi ends at some point, and wherever there would usually be a 9, the digit is instead a 1. This new number candidate for pi is infinite, doesn’t repeat and contains all the known properties of pi.
Therefore, it is possible that not any finite sequence of non-repeating numbers would appear somewhere in Pi.