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Biology OP (mander.xyz)

submitted 11 months ago* (last edited 11 months ago) by [email protected] to c/[email protected]

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[–] [email protected] 71 points 11 months ago* (last edited 11 months ago) (13 children)

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.

[–] [email protected] 7 points 11 months ago (8 children)

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.

[–] [email protected] 4 points 11 months ago (6 children)

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.

[–] [email protected] 3 points 11 months ago (1 children)

Addition by the additive inverse.

[–] [email protected] 1 points 11 months ago (1 children)

Now you just replaced one incalculable thing with a different incalculable thing.

[–] [email protected] 1 points 11 months ago (1 children)

Eh?

[–] [email protected] 2 points 11 months ago (1 children)

Computers don't subtract, and you can't just add a negative, a computer can't interpret a negative number, it can only store a flag that the number is negative. You need to use a couple addition tricks to subtract to numbers to ensure that the computer only has to add. It's addition all the way down.