Editing Indicator function (section)

==Definition==
Given an arbitrary set {{mvar|X}}, the indicator function of a subset {{mvar|A}} of {{mvar|X}} is the function
<math display=block>\mathbf{1}_A \colon X \mapsto \{ 0, 1 \}</math>
defined by
<math display="block" qid="Q371983">\operatorname\mathbf{1}_A\!( x ) =
\begin{cases}
1 & \text{if } x \in A \\
0 & \text{if } x \notin A \,.
\end{cases}
</math>

The [[Iverson bracket]] provides the equivalent notation <math>\left[\ x\in A\ \right]</math> or {{nobr|{{math|⟦&thinsp;''x'' ∈ ''A''&thinsp;⟧}},}} that can be used instead of <math>\mathbf{1}_{A}\!(x).</math>

The function <math>\mathbf{1}_A</math> is sometimes denoted {{math|𝟙{{sub|''A''}}}}, {{mvar|I<sub>A</sub>}}, {{mvar|&chi;<sub>A</sub>}}{{efn|name=χαρακτήρ|
The [[Greek alphabet|Greek letter]] {{mvar|&chi;}} appears because it is the initial letter of the Greek word {{lang|grc|{{math|χαρακτήρ}}}}, which is the ultimate origin of the word ''characteristic''.
}} or even just {{mvar|A}}.{{efn|
The set of all indicator functions on {{mvar|X}} can be identified with the set operator <math>\mathcal{P}(X),</math> the [[power set]] of {{mvar|X}}. Consequently, both sets are denoted by the conventional [[abuse of notation]] as <math>2^X,</math> in analogy to the relation for the count of elements in the powerset and the original set. This is a special case <math>\left(Y = \{0,\, 1\}\right)</math> of the notation <math>Y^X</math> for the set of all functions <math>f</math> such that <math>f: X \mapsto Y \,.</math>
}}