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In order to formalize these ideas, it is helpful to have notational devices for switching back and forth among different ways of exemplifying what is abstractly the same contents of information, in particular, for translating among sets, their logical expressions, and their functional indications.

In order to formalize these ideas, it is helpful to have notational devices for switching back and forth among different ways of exemplifying what is abstractly the same contents of information, in particular, for translating among sets, their logical expressions, and their functional indications.

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Given a set <math>X\!</math> and a subset <math>A \subseteq X,\!</math> let the ''selector function of <math>A\!</math> in <math>X\!</math>'' be notated as <math>A^\sharp\!</math> and defined as follows.

If S c X is a set contained in a universal set or domain X, then "S#", read as "S sharp" or "S selective", denotes the "selector function" of S, defined as:

S# : X > B with S#(x) = 1 iff x C S.

A^\sharp : X \to \mathbb{B} & \text{where} & A^\sharp (x) = 1 \iff x \in A.

Other names for the same concept, appearing under various notations, are the "indicator function" or the "characteristic function" of a set.

Other names for the same concept, appearing under various notations, are the ''characteristic function'' or the ''indicator function'' of <math>A\!</math> in <math>X\!</math>.

Conversely, if one has a binary valued function f : X  > B, then "f#", read as "f numbd" or "f selection", denotes the "selected set" of f, defined as:

Conversely, if one has a binary valued function f : X  > B, then "f#", read as "f numbd" or "f selection", denotes the "selected set" of f, defined as: