Sets and Functions

Abstract

We shall use the standard terms and notations of analysis and set theory. (Thus much of the following has already appeared in the first few pages of Analysis.) ℝ is the set of all real numbers, and ℤ is the set of all integers. If A is a set, then x ∈ A means that x belongs to A. If x does not belong to A, then we write x ∉ A. Let S be a set. Then

$$\left\{ {x\left| {x\; \in \;s\;and\;\left( \ldots \right)} \right.} \right\}$$

denotes the set of all elements of S that satisfy the condition (…). Thus the union of two sets A and B is

$$A\; \cup \;B\; = \;\left\{ {x\left| {x\; \in \;A\;or\,x\, \in \;B} \right.} \right\}.$$