Mapping two integers to one, in a unique and deterministic way

Question

Imagine two positive integers A and B. I want to combine these two into a single integer C.

There can be no other integers D and E which combine to C. So combining

Answer 1

For positive integers as arguments and where argument order doesn't matter:

1. Here's an unordered pairing function:

    = x * y + trunc((|x - y| - 1)^2 / 4) = 
   

2. For x ≠ y, here's a unique unordered pairing function:

    = if x < y:
              x * (y - 1) + trunc((y - x - 2)^2 / 4)
            if x > y:
              (x - 1) * y + trunc((x - y - 2)^2 / 4)
          =