characteristic function

In mathematics, characteristic function can refer to any of several distinct concepts:The most common and universal usage is as a synonym for indicator function, that is the functionwhich for every subset A of X, has value 1 at points of A and 0 at points of X − A.When applied to a natural number an effective procedure determines correctly if a natural number is or is not in the procedure's "set": "The characteristic function is the function that takes the value 1 for numbers in the set, and the value 0 for numbers not in the set" (cf Boolos-Burgess-Jeffrey (2002) p. 73).
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<mathematics> The characteristic function of set returns True if its argument is an element of the set and False otherwise.
(1995-04-13)