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The infinite sum of powers of 2 indeed diverges in the real numbers. However, in the 2-adic numbers, it does actually equal -1. https://en.wikipedia.org/wiki/P

by xigoi 3y ago

The infinite sum of powers of 2 indeed diverges in the real numbers. However, in the 2-adic numbers, it does actually equal -1. https://en.wikipedia.org/wiki/P-adic_number https://en.wikipedia.org/wiki/P-adic_number

Dylan16807 3y ago
Eh, P-adic numbers basically write the digits backwards, so "-1" has very little relation to a normal -1.
- xigoi 3y ago
  -1 means that when you add 1, you get 0. And the 2-adic number …11111 has this property.
- mike_hock 3y ago
  Any ring automatically gains all integers as meaningful symbols because there is exactly one ring homomorphism from Z to the ring.