When they say "applied twice", they're not talking about two independent applications to the same initial value. (That's a test for functional purity, not idemp

When they say "applied twice", they're not talking about two independent applications to the same initial value. (That's a test for functional purity, not idempotence.) Instead, they're referring to the following sequence of actions: 1. Update the value x according to the operation f. 2. Update the value x according to the operation f.