If by [1..N ⟶ 1..N] you mean the set of functions from [1..N] that have values in [1..N], I think you are wrong. The formula in the post describes a subset, the set of such functions that are surjective.
Yeah I think your right, in this context I saw the case of [ A -> B ] as a function from coimage A to image B which are all bijective. But it is meant as the more standard domain A to codomain B.
His natural language description is somewhat lacking in that aspect
> I had already explained that [1..N ⟶ 1..N] is the set of functions that map the set 1..N of integers from 1 through N into itself,
His natural language description is somewhat lacking in that aspect
> I had already explained that [1..N ⟶ 1..N] is the set of functions that map the set 1..N of integers from 1 through N into itself,