> Cantor's second proof generalises [...] That may be true, but at the time a student first sees this proof, you're trying to convince him that there are diffe

> Cantor's second proof generalises [...] That may be true, but at the time a student first sees this proof, you're trying to convince him that there are different cardinalities of infinity in the first place. In fact, you've probably showed them that there are as many integers as there are even integers, which works to establish an intuition that all infinite sets have the same size.