Idempotence: Difference between revisions

Revision as of 13:52, 23 December 2008

Citable Version ^[?]

This editable Main Article is under development and subject to a disclaimer.

[edit intro]

In mathematics idempotence is the property of an operation that repeated application has no further effect.

A binary operation $\star$ is idempotent if

x\star x=x

for all x:

equivalently, every element is an idempotent element for $\star$ .

Examples of idempotent binary operations include join and meet in a lattice; union and intersection on sets; disjunction and conjunction in propositional logic.

A unary operation (function from a set to itself) π is idempotent if it is an idempotent element for function composition, π² = π.

Revision as of 11:50, 23 December 2008 (view source) imported>Richard Pinch (added examples) ← Older edit		Revision as of 13:52, 23 December 2008 (view source) imported>Howard C. Berkowitz No edit summary Newer edit →
Line 1:		Line 1:
			{{subpages}}
	In [[mathematics]] '''idempotence''' is the property of an [[operation (mathematics)\|operation]] that repeated application has no further effect.		In [[mathematics]] '''idempotence''' is the property of an [[operation (mathematics)\|operation]] that repeated application has no further effect.