[jhuni]

> You misread me. What I said was that "set theory" is the general mathematical framework exactly equal to what we computer scientists call "type theory".

That makes more sense. I am coming from a mathematical background and not a computer science background myself.

> Mathematicians deal with sets, countable or otherwise, algebraic manipulations of them, bijective mappings, etc.

That is true. As a combinatorist I am one of those people who mainly focuses on countable sets. The isomorphism classes of sets (the counting numbers) are at the foundation of everything I do in combinatorics but other areas of mathematics (e.g topology) have very different approaches.