• hydroptic@sopuli.xyz
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    8 months ago

    And mathematicians divide by multiplying!

    In formal definitions of arithmetics, division can be defined via multiplication: as a simplified example with real numbers, because a ÷ 2 is the same as a × 0.5, this means that if your axioms support multiplication you’ll get division out of them for free (and this’ll work for integers too, the definition is just a bit more involved.)

    Mathematicians also subtract by adding, with the same logic as with division.

    • bort@feddit.de
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      8 months ago

      if your axioms support multiplication you’ll get division out of them for free

      this is true… except when it isn’t.

      In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist

      https://en.wikipedia.org/wiki/Ring_(mathematics)

      • hydroptic@sopuli.xyz
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        8 months ago

        Yeah I should maybe just have written

        if your axioms support multiplication you’ll get division out of them for free*

        *certain terms and conditions may apply. Limited availability in some structures, North Korea, and Iran. Known to the state of California to cause cancer or reproductive toxicity

    • meowMix2525@lemm.ee
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      8 months ago

      Right. The cells are dividing in half, which would be represented in math form by 1/0.5 = 2. Dividing by one half is the same thing as multiplying by 2, and division in general is really just a visually simplified way to multiply by a fraction of 1.

      Any time you divide by some fraction of 1, you will necessarily end up with a larger number because you’re doubling that division which reverses it back into multiplication, much in the same way as a negative x negative = positive. If that makes sense.

      A mathematician would not be bothered by this. A high schooler taking algebra I might be though, if you phrased it the same way this post did.

    • Kogasa@programming.dev
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      8 months ago

      a/b is the unique solution x to a = bx, if a solution exists. This definition is used for integers, rationals, real and complex numbers.

      Defining a/b as a * (1/b) makes sense if you’re learning arithmetic, but logically it’s more contrived as you then need to define 1/b as the unique solution x to bx = 1, if one exists, which is essentially the first definition.

      • Artyom@lemm.ee
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        8 months ago

        That’s me, a degree-holding full time computer scientist, just learning arithmetic I guess.

        Bonus question: what even is subtraction? I’m 99% sure it doesn’t exist since I’ve never used it, I only ever use addition.

      • hydroptic@sopuli.xyz
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        8 months ago

        Defining a/b as a * (1/b) makes sense if you’re learning arithmetic

        The example was just to illustrate the idea not to define division exactly like that