ELI5?

From Wikipedia, which agrees with you...

> A unary operation (or function) is idempotent if, whenever it is applied twice to any value, it gives the same result as if it were applied once; i.e., ƒ(ƒ(x)) ≡ ƒ(x). For example, the absolute value function, where abs(abs(x)) ≡ abs(x).

So is f(x) = x + 1 idempotent?

Under this part: "whenever it is applied twice to any value, it gives the same result as if it were applied once" it would appear so. f(2) = 3 f(2) still = 3.

But under this part: "ƒ(ƒ(x)) ≡ ƒ(x)"

f(f(x)) == f(f(2)) == f(3) = 4

Where'd I go wrong?