idempotence

Idempotence is a property that an operation in mathematics or computer science may have.

Idempotence implies reentrancy, but the converse is not necessarily true.

There are several meanings of idempotence, depending on what the concept is applied to:

The shadow of a point of the paper sheet is the point itself (idempotence).

The floor, ceiling, and fractional part functions are Idempotence:

The word idempotence was made by Benjamin Pierce because he saw the concept when studying algebra.

Idempotence: Whenever the operands of the operation are the same, the connective gives the operand as the result.

If the second axiom, that of idempotence, is relaxed, then the axioms define a preclosure operator.

A simple application of ordinal parity is the idempotence law for cardinal addition (given the well-ordering theorem).

Commutativity and associativity of assure (1), idempotence, (2).

The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost.

Through this correspondence, set-theoretic intersection shares several properties with logical conjunction, such as associativity, commutativity, and idempotence.

Idempotence: The closure of the closure of a set is equal to the closure of that set.

Exchange principle: If , then (and hence by Montonicity and Idempotence in Fact ).

In Event Stream Processing, idempotence refers to the ability of a system to produce the same outcome, even if an event or message is received more than once.

Idempotence of and can be visualized by sliding the two circles together and noting that the shaded area then becomes the whole circle, for both and .

It has the axioms of BL plus an axiom of idempotence of conjunction, and its models are called G-algebras.

More generally, every median graph gives rise to a ternary operation m satisfying idempotence, commutativity, and distributivity, but possibly without the identity elements of a distributive lattice.

Also, the following usual Boolean properties hold: excluded middle and (for conjunction and disjunction) associativity, commutativity, distributivity, De Morgan's laws, and idempotence.

Interestingly, from the idempotence of projection matrix, we can verify that the pseudoinverse of block matrix consists of pseudoinverse of projected matrices:

LULU smoothers are compared in detail to median smoothers by Jankowitz and found to be superior in many aspects, particularly in mathematical properties like idempotence.

In the HyperText Transfer Protocol (HTTP), idempotence and safety are the major attributes that separate HTTP verbs.

Reentrancy is not the same thing as idempotence, in which the function may be called more than once yet generate exactly the same output as if it had only been called once.

Lulu operators have a number of attractive mathematical properties, among them idempotence - meaning that repeated application of the operator yields the same result as a single application - and co-idempotence.

We define a topology on by declaring the closed sets to be the fixed points of the closure map (hence by idempotence and monotonicity is the (topological) closure of .)