Comments for Built on Facts

Comment on Everything in Pi… maybe. by acne

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Comment on Everything in Pi… maybe. by Annonymous

Annonymous — Fri, 19 Apr 2013 15:17:15 +0000

Whether pi is normal or absolutely normal is a question which appears totally beyond present day understanding. Borel’s argument shows that a “randomly picked” real number is absolutely normal with probability one but pi is not exactly “randomly picked”.

Comment on Everything in Pi… maybe. by Ori Vandewalle

Ori Vandewalle — Thu, 18 Apr 2013 17:30:03 +0000

The obvious answer is that, by the 23rd century, they’ve proven pi is normal. Sulu is just reporting this to us.

Comment on Everything in Pi… maybe. by doug bennion

doug bennion — Thu, 18 Apr 2013 15:46:58 +0000

Thank you Annonymous, I understand. I’m not a mathematician, but infinity is fun. At some point in the expansion of pi, it must repeat the prior sequence of numbers. Call that sequence S1. So pi = S1S1 … Then there must be another sequence S2 such that pi = S2S2S2 … Ultimately you have an infinite repeating decimal so pi is rational. lol never mind.

Comment on Everything in Pi… maybe. by Annonymous

Annonymous — Wed, 17 Apr 2013 15:01:56 +0000

Note that if every finite sequence occurs at least once then every finite sequence occurs infinitely often

Comment on Everything in Pi… maybe. by Annonymous

Annonymous — Wed, 17 Apr 2013 13:24:56 +0000

Doug – For what Takei says to be true it suffices that every finite sequence of digits occurs at least once in the decimal expansion of pi. This is a much weaker condition than normality to base 10. It is easy to define decimal expansions in which almost all digits are zero but every finite sequence of digits occurs infinitely often.

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