abstractmath.org 2.0
help with abstract math

Produced by Charles Wells     Revised 2017-02-22
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This is the head of the chapter on Sets.

The concept of set was introduced in the late nineteenth century by Georg Cantor. It was initially fiercely resisted, but has had such clarifying power that it is now used everywhere in mathematics.

Informally, a set is a collection of items. The items which constitute a particular set are called the elements or members of the set.

This chapter is not an introduction to the theory of sets. Its purpose is to introduce people new to abstract math to the basic ideas and terminology concerning sets and to the cognitive difficulties the notion of set causes some students to have.


Many math texts and teachers give examples of sets whose elements are not math objects, for example the set of Presidents of the United States. I rarely do that on this website. Such sets are abstract objects but not math objects in the sense used in abstractmath.org (they may vary with time, for example).

Table of contents

Sets: Notation

Some specific sets

Sets: Specification

Subsets and inclusion

Sets: Rules of Inference

Sets: Metaphors and images

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