Editing Complement (set theory) (section)

=== Definition ===
If {{math|''A''}} and {{math|''B''}} are sets, then the '''relative complement''' of {{math|''A''}} in {{math|''B''}},<ref name="Halmos-1960">{{harvnb|Halmos|1960|p=17}}.</ref> also termed the '''set difference''' of {{math|''B''}} and {{math|''A''}},<ref>{{harvnb|Devlin|1979|p=6}}.</ref> is the set of elements in {{math|''B''}} but not in {{math|''A''}}.
[[File:Relative compliment.svg|thumb|230x230px|The '''relative complement''' of {{math|''A''}} in {{math|''B''}}: <math>B \cap A^c = B \setminus A</math>]]
The relative complement of {{math|''A''}} in {{math|''B''}} is denoted <math>B \setminus A</math> according to the [[ISO 31-11#Sets|ISO 31-11 standard]]. It is sometimes written <math>B - A,</math> but this notation is ambiguous, as in some contexts (for example, [[Minkowski addition|Minkowski set operations]] in [[functional analysis]]) it can be interpreted as the set of all elements <math>b - a,</math> where {{math|''b''}} is taken from {{math|''B''}} and {{math|''a''}} from {{math|''A''}}.

Formally:
<math display=block>B \setminus A = \{ x\in B : x \notin A \}.</math>