ZFC and the foundation of mathematics
Today I've been studying ZFC:
and I have one particular issue I'm not clear on. It seems that ZFC by itself only allows for sets as the mathematical objects that exist. On the other hand, it is said that ZFC can serve as a foundation for most of mathematics. I'm curious, how then can ZFC be used to talk about say, Calculus and the real numbers?
I have read a bit about "ur-element" but they seem to be peripheral and not central to ZFC itself. Could somebody explain?