= Indicator Functions =

'''Indicator functions''' are [[Analysis/Functions|functions]] defined on a [[Analysis/Sets|set]]; it maps a subset to 1 and everything else to 0.

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== Description ==

For a set ''A'', an indicator function is ''1,,B,, : A -> {0,1}'' where for every ''x ∈ A'', ''f(x) = 1'' if ''x ∈ B'', else 0.

As a concrete example, the '''Dirichlet function''' indicates the subset of [[Analysis/Sets#Commonly_Used_Sets|real numbers]] that are rational numbers. It is notated as ''1,,Q,,'' to mean that ''1,,Q,,(x) = 1'' if ''x ∈ Q'', else 0.

Another common notation used for the set of real numbers is ''1,,(a,b),,(x)'', as in a function that maps ''x'' to 1 if ''a ≤ x ≤ b'', else 0.



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CategoryRicottone