The above meaning derives from the following meaning in mathematics. A function f from a set S to itself is idempotent if f o f = f, that is, f(f(x)) = f(x) for all x in S. This is equivalent to saying that f(x) = x for all x in f(S). Trivial examples of idempotent functions on S are the identity map and the constant maps. Less trivial examples are the absolute value function of a real or complex argument, and the closure operator for a topological space X, which is an idempotent function on the power set of X.
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