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In mathematics, '''characteristic function''' can refer to any of several distinct concepts:
* The most common and universal usage{{citation-needed}} is as a synonym for [[indicator function]], that is the function
::<math>\mathbf{1}_A: X \to \{0, 1\}</math>
:which for a given subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''.
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