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Using a sledgehammer to crack a nut (i.imgur.com)
submitted 1 year ago by genfood@feddit.de to c/science_memes@mander.xyz
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[-] Eufalconimorph@discuss.tchncs.de -2 points 1 year ago

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?

[-] Rin@lemm.ee 8 points 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

[-] kogasa@programming.dev 8 points 1 year ago* (last edited 1 year ago)

There's only 2. sqrt(-1) isn't a solution. There are at most 2 over any integral domain.

this post was submitted on 02 Oct 2023
218 points (97.4% liked)

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