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.
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
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
