I've heard that there is a bit of argument over whether you can confirm that $\pi$ is truly irrational. We know $\pi$ up to 2.7 trillion digits, but that accuracy isn't even that big, especially when you compare it to how accurately we know $e$. So, is there a possibility that the digits of $\pi$ will repeat or end?
2026-05-16 04:07:44.1778904464
Irrationality of $\pi$ isn't confirmed?
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You can't prove irrationality by calculating digits and looking for a repeat because the repeat could start a little further out. $\pi$ and $e$ are known to be transcendental, not just irrational. You may have heard that we don't know if $\pi$ is normal, meaning any sequence of digits occurs with the correct limiting probability. That is correct, but most people who understand it would guess that it is.