Baby Rudins chapter 1 assumes familiarity with the arithmetic of natural numbers and rational numbers. Rudin constructs the reals and complex numbers from the rational numbers.
For curiosity's sake, I would like to see treatment from either an axiomatization of natural numbers (Peano) or construction (via ZFC). Is there a rigorous book that constructs the number systems along with the necessary objects like functions, relations, cardinalities in a comprehensive and rigorous fashion? Looking for a rigorous style more than a sketch or chatty style.