• Valmond@lemmy.world
    link
    fedilink
    arrow-up
    1
    arrow-down
    1
    ·
    11 months ago

    A number divided by zero equals infinity.

    Except if it’s zero then (so 0/0) it is either undefined or any number IIRC.

    • Leate_Wonceslace@lemmy.dbzer0.com
      link
      fedilink
      English
      arrow-up
      1
      ·
      edit-2
      11 months ago

      No. The standard field (that is, a ring where both operations are abelian groups) on the complex numbers doesn’t have a multiplicative inverse of 0; rings can’t have a multiplicative inverse for the additive identity. You can create an algebra with a ring as a sub-algebra with such, but it will no longer be a ring. My preferred method is to impose such an algebra on the one-point compactification of the Complex Numbers, where the single added point is denoted as “Ω”.

      I started this project when I was 12, and when I could show that the results were self-consistent this was what I had settled on:

      let z be a complex number that is not otherwise specified by the following equations. Note: the complex numbers contain the Real numbers, and so the following equations apply to the them as well.

      0Ω=Ω0=1

      z+Ω=Ω+z=zΩ=Ωz=Ω=ΩΩ

      Ω-Ω=0. Ω-Ω=Ω+(-Ω)=Ω+(-1Ω)=Ω+Ω=0

      The algebra described above is not associative. That is to say, (AB)C does not always equal A(BC).

    • bizarroland@fedia.io
      link
      fedilink
      arrow-up
      1
      ·
      11 months ago

      If you plot out any number divided by x, as x approaches 0 the answer goes towards Infinity, yes.

      When it reaches zero it ceases to be a number.

      Every number divided by 0 is “undefined”, and it is not undefined because we can’t describe it, it is undefined because it does not exist, because you cannot divide things by 0.