Gollum to Science [email protected]English • 1 year agoUsing a sledgehammer to crack a nuti.imgur.comimagemessage-square7fedilinkarrow-up1218arrow-down16
arrow-up1212arrow-down1imageUsing a sledgehammer to crack a nuti.imgur.comGollum to Science [email protected]English • 1 year agomessage-square7fedilink
minus-square@[email protected]linkfedilinkEnglish-2•1 year agoWell, 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?
minus-squareKogasalinkfedilinkEnglish8•edit-21 year agoThere’s only 2. sqrt(-1) isn’t a solution. There are at most 2 over any integral domain.
minus-square@[email protected]linkfedilinkEnglish8•1 year agonot 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
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?
There’s only 2. sqrt(-1) isn’t a solution. There are at most 2 over any integral domain.
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 = -1supposing x was √-1:
(√-1)² -1 = 0 -1 -1 = 0 -2 = 0therefore we can certainly conclude that x ≠ √-1