Right Operation is Idempotent

Theorem

The right operation is idempotent:

$\forall x: x \rightarrow x = x$

Proof

Immediate from the definition of the right operation.

Also see

• Left Operation is Idempotent

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Exercise $2.17 \ \text{(a)}$