CTK Insights

19 Jan

p-adic Curiosities

Wonderment at the identity

-1 = 1 + 2 + 4 + 8 + ...

dwarfes the perennial question as to whether .9999... equals 1 or not. Still, it holds in exactly same sense as the limit of a convergent series. The sums of the successive powers of 2 converge in the 2-adic norm! Moreover, they converge to a negative 1.

See, p-adic Numbers and p-adic Expansions

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