# idempotent

(*not comparable*)

- (mathematics, computing) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.
- A projection operator is idempotent.
- Every finite semigroup has an idempotent element.

- (mathematics)
*Said of an element of an algebraic structure (such as a group or semigroup) with a binary operation*: that when the element operates on itself, the result is equal to itself.- Every group has a unique idempotent element: namely, its identity element.

- (mathematics)
*Said of a binary operation*: 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, then it distributes with respect to itself. (This is useful for understanding one of the conjunction rules of simplification to Prenex Normal Form, if the universal quantifier is thought of as a "big AND".)

Contrast with *nullipotent*, meaning has *no* side effects - doing it multiple times is the same as doing it *zero* times, rather than *once,* as in idempotent.

## idempotent - Computer Definition

An operation that produces the same results no matter how many times it is performed. For example, a database query that does not change any data in the database is idempotent. Functions can be designed as idempotent if all that is desired is to ensure a certain operation has been completed. For example, with an idempotent delete function, if a request to delete a file is successfully completed for one program, all subsequent requests to delete that file from other programs would return the same success confirmation message. In a non-idempotent delete function, an error would be returned for the second and subsequent requests indicating that the file was not there.