Nor is it obvious how multiplication of apples should work. Apples might be considered an infinite cyclic abelian monoid, if you like, but it’s beside the point—the point is that once you know what axioms they satisfy, you now know a whole bunch of stuff.
Well, if you have a row of 3 apples, and you get another three rows, you’ll have 9 apples. But multiplying 3 apples by 3 apples would result in 9 apples^2; and I don’t know what those look like.
Nor is it obvious how multiplication of apples should work. Apples might be considered an infinite cyclic abelian monoid, if you like, but it’s beside the point—the point is that once you know what axioms they satisfy, you now know a whole bunch of stuff.
Well, if you have a row of 3 apples, and you get another three rows, you’ll have 9 apples. But multiplying 3 apples by 3 apples would result in 9 apples^2; and I don’t know what those look like.