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The infinite sum involving powers of two is actually true in the 2-adic integers.
by suremarc 4y ago
The infinite sum involving powers of two is actually true in the 2-adic integers.
- solresol 4y agoAnd 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.
- kevinventullo 4y agoYep, 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/ https://kevinventullo.com/