There seem to be at least three meanings of "idempotence": 1. Some x is idempotent relative to f if: f(x, x)=x 2. Some f is idempotent if for all x: f(x

There seem to be at least three meanings of "idempotence": 1. Some x is idempotent relative to f if: f(x, x)=x 2. Some f is idempotent if for all x: f(x, x)=x 3. Some f is idempotent if for all x: f(f(x))=f(x)