I think they are used everywhere because you can describe everything with them easily. I mean i still prefer a set of points over a newly introduced definition

I think they are used everywhere because you can describe everything with them easily. I mean i still prefer a set of points over a newly introduced definition of a "circle" just to be able to express a problem in mathematical language. It's kind of the same for functions too, they're used to describe so many things sometimes in a weird context too. I think the best abstraction is that which creates as little mental overhead as possible. Sets and relations are pretty basic and simple in that regard.