Meaning of notation $\textbf{1}_{\{x \in S\}}$

Question

Came across this notation today which I've never seen before. It was used with no explanation. For the equation to make sense, I think $\textbf{1}_{\{x \in S\}}$ means, "It takes the value 1 for $x \in S$ and $0$ otherwise." I.e., it is like an indicator function. Is this correct/common notation?

Your interpretation is correct. This is fairly standard notation for a characteristic or indicator function — lulu, Jan 20 '20 at 17:19
I have never seen this before until now. It does appear to be a clever way of convention to abbreviate concisely. — Mr Pie, Jan 20 '20 at 17:25

score 4 · Accepted Answer · answered Jan 20 '20 at 17:20

4

You got it. Personally I know of $\mathbb 1_X$ and $\chi_X$ as notation for the indicating function of a set.

answered Jan 20 '20 at 17:20

Jonas Linssen

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Meaning of notation $\textbf{1}_{\{x \in S\}}$

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