4 ms·
> The problem with multiplication is not that the proofs fall apart, it is that multiplication does not mean what you want it to mean. Well, yeah, that's kind
by lisper 2y ago
> The problem with multiplication is not that the proofs fall apart, it is that multiplication does not mean what you want it to mean.
Well, yeah, that's kind of the point: the positiveness of the naturals is not just a convention, it is actually a logical consequence of something in the axioms. Specifically, it is a logical consequence of the definition of multiplication. I find that interesting.
- btilly 2y agoThat ties to one of the standard axioms of the real numbers in classical mathematics. There exists a set P which is closed under addition and multiplication, such that for every real number x, one of these three things is true: x is in P, -x is in P, x = 0. P is, of course, the positive numbers. This axiom makes the reals into an ordered field. Add in completeness, and the reals are unique (up to choice of set theory).