A mapping f: X → Y is a one-to-one correspondence if f is one-to-one and onto. This is equivalent to saying that for each y ∈ Y, f^(-1){y} has precisely one element. If f: X → Y is a one-to-one correspondence, we can define an inverse mapping Y → X which is also a one-to-one correspondence. In fact, we simply have f^(-1) = {(y,x) ∈ Y × X | f(x) = y}. It follows that y = f(x) if and only if x = f^(-1)(y). Note that (f^(-1))^(-1) = f.
Let {1,2, ..., k} be a set. Define a one-to-one correspondence from Nₖ × Nₑ to Nₖₑ.
