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
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
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.
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.
this is true… except when it isn’t.
https://en.wikipedia.org/wiki/Ring_(mathematics)
Yeah I should maybe just have written
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.
Cells: 🫣🫨😢