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   myrmepropagandist (futurebird@sauropods.win)'s status on Sunday, 22-Jan-2023 04:06:18 JST myrmepropagandist

   What is something you learned in math that made you loose a sense of innocence-- knowledge that you can never unlearn that changes the world forever?

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     Alexandre Oliva (lxo@gnusocial.net)'s status on Sunday, 22-Jan-2023 04:06:17 JST Alexandre Oliva

     in reply to
     at some point I was told that the decimal (or any other base) expansion of such irrational numbers as $\Pi$ contained any other number
     but that can't be! if it contained all of the digits of $\Pi$, in sequence, in its fractional part, then the sequence of digits of $\Pi$ would be a repeating sequence, therefore it would be rational rather than irrational!
     indeed, even rational numbers with a periodic component to their fractional expansion cannot fit in the expansion of $\Pi$
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     ceoln (ceoln@qoto.org)'s status on Monday, 23-Jan-2023 14:22:43 JST ceoln

     in reply to

     • Alexandre Oliva

     @lxo

     This sounds like the claim that Pi is "normal" in a particular base. It's not actually known whether Pi is normal in any particular base, I don't think, but in some sense most real numbers are. It doesn't say that every other number is contained somewhere in pi, just that any finite string of digits is. So no irrational or repeating numbers required, if I have it right.

     @futurebird

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     ceoln (ceoln@qoto.org)'s status on Monday, 23-Jan-2023 14:23:00 JST ceoln

     in reply to

     • Alexandre Oliva

     @lxo

     This addresses inter alia the claim that every (finite?) string of numbers appears somewhere in Pi. https://en.m.wikipedia.org/wiki/Normal_number

     @futurebird

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     Jorge Stolfi (jorgestolfi@mas.to)'s status on Monday, 23-Jan-2023 14:23:23 JST Jorge Stolfi

     in reply to

     • Alexandre Oliva

     @lxo @futurebird

     It is expected to contain every FINITE sequence of digits.

     It cannot contain every INFINITE sequence of digits, because such a sequence would have to be all digits of Pi after a certain position. The number of of such positions is aleph-0 (the cardnality of integer numbers) while the number of distinct infinite sequences is aleph-1 (the cardinality of real numbers).

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