Idempotency means f(x) = f(f(x)).* Here x is interpreted as state and f an action acting on the state. State is in practice always subjected to side effects and concurrency. That's why if x is state then f can never be purely idempotent and the term has to be interpreted in a hand-wavy fashion which leads to confusions regarding attempts to handle that mismatch which again leads to rather meandering and confusing and…
That is simply not true. f could be, for example, “set x.variable to 7”, which is definitely idempotent.