Well, Cantor's diagonalization argument can be used to prove the Halting theorem, which is another problem that is easy to state and is very interesting to thin

Well, Cantor's diagonalization argument can be used to prove the Halting theorem, which is another problem that is easy to state and is very interesting to think about. The notion of the cardinality of sets comes up everywhere in mathematics, and often enough you end up showing that something holds up to a countable number of exceptions. These two kinds of infinities - cardinality of naturals and reals - are so pervasive, you can't get away from them. But you can do a lot of math without ever having to deal with the ordinal numbers. For that reason, cardinals are more interesting to me - not just as a concept in and of itself.