Let's dissect this function really quickly, first we define the set of integers:
Ok, now we will define the Cartesian Product of itself, which I will call :
So, now we have what we need to define our function, which is:
This is a binary function defined by:
So, the range consists of all the products of the integers which is a subset of , and the domain consists of any pair of integers.
It can't be one-to-one because and are equinumerous, so the range of the function is also a subset of , and can therefore cover the entire range, and so it is onto.