[cma]

I'd start with Discrete Mathematics before Spivak. From what I remember, Spivak jumps in to constructing the reals out of set theory pretty quickly.

A discrete math text will drill you over a lot more basic proofs involving set theory that would help in understanding his construction.

[WallWextra]

Construction of the reals is in an appendix at the back. He starts with ordered field axioms.

Frankly there's something about the presentation in "discrete math" books that I find much more confusing and difficult than Spivak, which is just talking logically about numbers and their properties.