The indicator function of a subset {{mvar|A}} of a set {{mvar|X}} is a function
<math display=block>\mathbf{I1}_A \colon X \to \{ 0, 1 \} </math>
defined as
<math display=block>\mathbf{I1}_A(x) :=
\begin{cases}
1 ~&\text{ if }~ x \in A~, \\
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</math>
The [[Iverson bracket]] provides the equivalent notation, <math>[x\in A]</math> or {{nowrap|{{math|⧙ ''x'' ϵ ''A'' ⧘}},}} to be used instead of <math>\mathbf{I1}_{A}(x)\,.</math>
The function <math>\mathbf{I1}_A</math> is sometimes denoted {{mvar|I<sub>A</sub>}}, {{mvar|χ<sub>A</sub>}}, {{mvar|K<sub>A</sub>}}, or even just {{mvar|A}}.{{efn|name=χαρακτήρ|The [[Greek alphabet|Greek letter]] {{mvar|χ}} appears because it is the initial letter of the Greek word {{lang|grc|χαρακτήρ}}, which is the ultimate origin of the word ''characteristic''.}}{{efn|The set of all indicator functions on {{mvar|X}} can be identified with <math>\mathcal{P}(X),</math> the [[power set]] of {{mvar|X}}. Consequently, both sets are sometimes denoted by <math>2^X.</math> This is a special case (<math>Y = \{0,1\} = 2</math>) of the notation <math>Y^X</math> for the set of all functions <math>f:X \to Y.</math>}}
