3. Thinking continuously

Abstract

Many topologists might choose to describe their subject as the study of continuity. There are continuous and discontinuous functions in our everyday routines. ‘Thinking continuously’ aims to provide a more rigorous sense of what continuity entails for real-valued functions of a real variable. It focuses on functions having a single numerical input and a single numerical output. The properties of continuous functions are considered and the boundedness theorem and intermediate value theorem are also explained.