• EufalconimorphEnglish
    35·
    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.eeEnglish
      7·
      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.devEnglish
      7·
      1 year ago

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