Definition 5.20 (Compliments)

#Definition

The $complement$ of a set $A$ , short $\bar{A}$ , to be the set of all elements, that do not belong to $A$

To avoid Russel's Paradox (The set of all 5.1 Sets), we must define a Universe for which the compliment is set in.

Example

Let $U$ be our fixed universe, which itself is a set, and let $A \subseteq U$ be a set.
The $complement of A in U$ is the set $\bar{A} : = U - A$