@NovaliumCompany What sort of number? What do you want to use it for? E.g. there's an axiomatization of natural numbers via Peano axioms, and then a construction of the reals via Dedekind cuts, But there's also a notion of
real closed fields that you can substitute in many places for the "actual reals". Then there's category theoretic definitions as natural number objects and terminal archimedic fields...
In this answer we give a proof of Goldstone's theorem at the physics level of rigor following Ref. 1:
We are given a spacetime-translation-covariant 4-current
$$\hat{J}^{\mu}(x)~=~e^{i(\hat{H}t-\hat{\bf P}\cdot {\bf x})}
\hat{J}^{\mu}(0)e^{i(\hat{\bf P}\cdot {\bf x}-\hat{H}t)} \tag{1}$$
that sa...
