[lupire]

Idempotent means that repeating the same operation eventually stabilizes, not that Op^2 = Op. It combines retryability of failures with retryability of successes.

Alternatively, idempotency applies to successful operations, orthogonal from error cases.

Retryability doesn't help in the case of the (bad) operation "+1" which is not idempotent.

[wnoise]

Idempotent means exactly Op^2 = Op. If you want a word that means those other things, go find another, this one has long been taken.