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Using a sledgehammer to crack a nut
(i.imgur.com)
Is that Bill Gates?
Yep, the poorer of the two dudes playing lol
sucks to be him
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?
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
There's only 2. sqrt(-1) isn't a solution. There are at most 2 over any integral domain.
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