>>11207675Technically you can make a relation out of any function (and vice-versa), however as I said, the point is that you're looking at different things.
When I say "function", I think of topological and analytical properties. (is it continuous ? is it analytical (in the complex planes) ? is it convex/concave, what equations does it obey, etc...)
When I say "relation", I think of algebraic and set theoretic properties (what are the classes of that set which verify the relation, ie, for all x, y in S, xRy")
The example I cited is a bit trivial as a relation, but at least it gives rise to the group Z/2Z and define parity (which is a useful algebraic concept).
As a function, "f(x, y) = 1 if x=y mod 2, 0 otherwise" has no real interesting properties. The "arrival" set isn't even Hausdorff.
