Definition:Idempotent/Operation

Definition

Let $\circ: S \times S \to S$ be a binary operation.

If all the elements of $S$ are idempotent under $\circ$, then the term can be applied to the operation itself:

The binary operation $\circ$ is idempotent iff:

$\forall x \in S: x \circ x = x$

Also see

Examples of idempotent operations:

• Set union: $\cup$
• Set intersection: $\cap$

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $2.17$