• @[email protected]
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    -21 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?

    • Kogasa
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      1 year ago

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

    • @[email protected]
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      81 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:

      (√-1-1 = 0
      -1 -1 = 0
      -2 = 0
      

      therefore we can certainly conclude that x ≠ √-1