Overview

One of the questions that accompanied the rigorous foundation of set theory at the end of the nineteenth century was the relationship of the relative sizes of the set of real numbers and the set of rationals. The axioms that had been laid down shortly thereafter were expected to provide an answer to the question of whether there was any infinite number between the sizes of those two sets. After an earlier proof that there might be a negative answer to the question, the work of Paul J. Cohen in the 1960s demonstrated that the question was not settled by the standard axioms. As a result, the notion of truth for statements about infinite sets was regarded as perhaps in need of revision.

Background

The notion of the infinite was one of the legacies of Greek philosophy...