History of Idempotent

	Revision 6 . . December 9, 2001 7:18 am by AxelBoldt
	Revision 5 . . December 9, 2001 6:35 am by Taw [example: abs()]
	Revision 4 . . September 30, 2001 6:41 pm by Zundark [expand 2nd paragraph]

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Changed: 3c3

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. A less trivial examples are absolute value of real or complex argument and the closure operator for a topological space X, which is an idempotent function on the power set of X.

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.