Comment by grandDesigns

In {f ∈ [1..N ⟶ 1..N] : ∀ y ∈ 1..N : ∃ x ∈ 1..N : f[x]=y}

What does the colon : mean?

It used to be that:

| = given that

, = and

but, I have never seen a : used in math.