I'm looking for a function where f(x1, x2) = f(x2, x1), but f(x1, x2) CANNOT equal any other f(xi, xj). Also, f() must also be reversible, so I could calculate xi from f(xi, xj) and xj. Can anyone think of such a function?
As an example, f() cannot be bitwise addition: bin3 + bin5 = bin8, but bin1 + bin7 = bin8 also.
edit: Thanks all. I'm just going with f(x1,x2) = implode(delimiter, sort(x1,x2)). I figured maybe there was a more elegant solution. The insights on bounding were good though. I would give upvotes all around but I don't have enough rep yet.