Definition of "idempotent" in English

adjective

1. (mathematics, computing) (said of a function) Such that, when performed multiple times on the same subject, it has no further effect on its subject after the first time it is performed.

   • A projection operator is idempotent.
   • An HTTP request using the PUT verb should be idempotent, so that it can be sent to the server any number of times with the same end result.

2. (mathematics) (said of an element of an algebraic structure with a binary operation, such as a group or semigroup) Such that, when it operates on itself, the result is equal to itself.

   • Every finite semigroup has an idempotent element.
   • Every group has a unique idempotent element: namely, its identity element.

3. (mathematics) (said of a binary operation) Such that all of the distinct elements it can operate on are idempotent (in the sense given just above).

   • Since the AND logical operator is commutative, associative, and idempotent, it distributes with respect to itself.

4. (mathematics) (said of an algebraic structure) Having an idempotent operation (in the sense given above).

noun

1. (mathematics) An idempotent element.

2. (mathematics) An idempotent structure.