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/
there is also a lot of good stuff concerning such computational tricks and their relation with 2-adics in section 7.1.3 (Bitwise Tricks and Techniques) of volume 4A of The Art of Computer Programming: https://www-cs-faculty.stanford.edu/~knuth/fasc1a.ps.gz
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[ 3.4 ms ] story [ 19.8 ms ] threadThose 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.
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/
there is also a lot of good stuff concerning such computational tricks and their relation with 2-adics in section 7.1.3 (Bitwise Tricks and Techniques) of volume 4A of The Art of Computer Programming: https://www-cs-faculty.stanford.edu/~knuth/fasc1a.ps.gz