As I understand it, a function maps the elements of one set on to the elements of another set. Here, F is a set of pairs of numbers whose sum is 10. F is an infinite set because there is no mention of what sets x and y belong to (e.g, integers, natural numbers, real numbers, etc.). I think it's neither a relation nor a function. x+y=10 is a linear function (mapping x to y or vice versa) but this function is an internal requirement of its elements, not a function itself.