Axioms of Infinity as the Starting Point for Rigorous Mathematics(<Special Section>Infinity in Philosophy and Mathematics)

Abstract

A more than sufficient starting point for the development of all currently accepted rigorous mathematics is provided by a pair of assumptions about how many individuals there are: the relative assertion that there are as many of them as there are small classes of them, and the absolute assertion that there are indescribably many of them. But explaining what the foregoing assertion means is more work than establishing that it is true.