Introduction

Every day we talk casually about 'collections' — the books on a shelf, the songs on a favourite playlist, the rules a school expects everyone to follow. Whenever such a collection is precise enough that we can always say for certain whether something belongs to it or not, mathematicians give it a special name: a set. The same idea of a well-defined collection shows up throughout mathematics too, in groups of numbers, functions, and equations. This chapter builds on that everyday intuition to define sets formally, learn how to writ …