That 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, s

That 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).