Editing Complement (set theory) (section)

=== Definition ===
If {{mvar|A}} is a set, then the '''absolute complement''' of {{mvar|A}} (or simply the '''complement''' of {{mvar|A}}) is the set of elements not in {{mvar|A}} (within a larger set that is implicitly defined). In other words, let {{mvar|U}} be a set that contains all the elements under study; if there is no need to mention {{mvar|U}}, either because it has been previously specified, or it is obvious and unique, then the absolute complement of {{mvar|A}} is the relative complement of {{mvar|A}} in {{mvar|U}}:<ref>The set in which the complement is considered is thus implicitly mentioned in an absolute complement, and explicitly mentioned in a relative complement.</ref>
<math display=block>A^c= U \setminus A = \{ x \in U : x \notin A \}.</math>

The absolute complement of {{mvar|A}} is usually denoted by <math>A^c</math>. Other notations include <math>\overline A, A',</math><ref name=":1" /> <math>\complement_U A, \text{ and } \complement A.</math><ref name="Bou">{{harvnb|Bourbaki|1970|p=E II.6}}.</ref>