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. |
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.
More generally, if S is a set with a binary operation * on it, then an element s of S is said to be idempotent if s * s = s. An idempotent element is often just called an idempotent. For example, any identity element is an idempotent. If every element of S is idempotent, then S itself (or the binary operation *) is said to be idempotent. For example, the operations of set union and set intersection are idempotent.