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erg art ink's avatar

The tech bros and the mathematicians before them have been trying to square the circle, since forever, and to this date they still have not solved the equation beyond a decimal approximation. π is unsolvable; math lists π as an irrational number.

The circle remains un broken, un squared.

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Joseph Rahi's avatar

Happy Pi day!

One small point of contention: I think it's not necessarily true that every finite sequence of digits exists somewhere in the digits of pi. It might intuitively appear that way because the digits are infinite and appear to be random. But if they are truly random, then there cannot be a preference for any infinite sequence of digits over any other, in which case all of the infinite sequences which lack our specified finite sequence have as good a chance as all those which contain it.

Looking at it digit by digit, it's clear that as we consider more random digits tending to infinity, the odds of a particular finite sequence not appearing tend towards 0. But that doesn't mean that we can say the odds actually are 0 when the number of digits equals infinity. If anything, I think we should consider the odds as infinitesimal, but not 0. I think we have to allow infinitesimals if we're to talk about infinite random sequences, as otherwise we find that every infinite sequence has a probability of 0... And then since there are infinite finite sequences, it's quite possible some of them might accomplish that infinitesimally unlikely feat of escaping pi.

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