Comment

Well, you’ve got 1. And -1. And sqrt(-1). And the unit pseudoscalars of the Clifford algebras for every number of dimensions.

So there are a countably infinite number of solutions. Can anyone find a bigger set? Something with an uncountably infinite set of solutions?

Sort:hotnew top

Rin@lemm.ee ⁨1⁩ ⁨year⁩ ago
not sure I’m following. there are only two solutions to this. the equation is essentially:

x² -1 = 0 x² = 1 x = ±√1 x = ±1 => x = 1, x = -1

supposing x was √-1:

(√-1)² -1 = 0 -1 -1 = 0 -2 = 0

therefore we can certainly conclude that x ≠ √-1
source
kogasa@programming.dev ⁨1⁩ ⁨year⁩ ago
There’s only 2. sqrt(-1) isn’t a solution.

source