Two's complement unexpectedly shows up in infinite series

Re:Two's complement unexpectedly shows up in infinite series by suremarc on Thursday October 20, 2022 @04:49PM (#33280494)

The infinite sum involving powers of two is actually true in the 2-adic integers.

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Re:Two's complement unexpectedly shows up in infinite series by solresol on Thursday October 20, 2022 @08:46PM (#33282787)

And any of his other examples would work with powers-of-p if p is prime.

Those infinite series aren't divergent if you are measuring their size p-adically.

Gouvea's book actually goes through the things that RobAlni has just discovered.

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Re:Two's complement unexpectedly shows up in infinite series by kevinventullo on Friday October 21, 2022 @01:35AM (#33284850)

Yep, and that last number is the 2-adic representation of -4/3.

It turns out a lot of ideas from calculus and real analysis carry over to the 2-adics, and this can lead to some interesting computational shortcuts since two’s complement is essentially native 2-adic arithmetic. I’ve blogged a bit about this here: https://kevinventullo.com/

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