Linear Algebra, 5th Edition

Appendices

Appendix A Sets

A set¹ is a collection of objects, called elements of the set. If x is an element of the set A, then we write $x\in A$; otherwise, we write $x\notin A$. For example, if z is the set of integers, then $3\in Z$ and ${\displaystyle \frac{1}{2}}\notin Z$.

¹It is impossible to give a formal definition of the word set in terms of simpler concepts. In this appendix we explain the conceptual ideas behind sets and the facts about them that we will use in this book.

One set that appears frequently is the set of real numbers, which we denote by R throughout this text.

Two sets A and B are called equal, written $A=B$, if they contain exactly the same elements. Sets may be described in one of two ways:

1. By listing the elements of the set between set braces $\left\{\right\}$.

2. By describing the elements ...