2
votes
2answers
145 views

Axioms for sets of numbers

What is the most common axiomatic system used by modern mathematicans for the properties of the integers, rationals, reals, and complex numbers? Or does one commonly use a single axiomatic system ...
3
votes
2answers
95 views

Does the negative axiom hold in a universe containing just 0 and 1?

I am self-studying the wonderful book, Elementary Geometry from an Advanced Standpoint. In chapter 1, problem 19 it says: Suppose that the elements of R were 0 and ...