This is only true to a point. In some sense, yes, the real numbers are the only complete & [canonically] totally-ordered field, up to isomorphism; but this last part is a bit of a snag for the language being used here, since the tools used to develop the real numbers in those different ways are certainly created as much as language & software are created.

You could cling to the idea that even these things are merely "discovered," but eventually you'd find yourself talking about the Platonic ideal of the wobbly, scratched up table in the neighbors' house, and how the carpenter originally discovered the Form of this particular table.

This is more a criticism of the English words for invention, creation, discovery, & the like; but then, philosophy of math that gets too far afield from actually doing logic is basically just philosophy of language.