Modern Mathematical Logic

Set theory originated in an attempt to understand and somehow classify small, or negligible, sets of real numbers. Cantor’s early explorations into the realm of the transfinite were motivated by a desire to understand the points of convergence of trigonometric series. The basic ideas quickly became a fundamental part of analysis, in addition to permeating many other areas of mathematics. Since then, set theory has become a way to unify mathematical practice, and the way in which mathematicians grapple with the infinite in all areas of mathematics.