It is quite surprising to most people when they first learn that there are more real numbers than there are integers, but there are just as many pairs of intege

It is quite surprising to most people when they first learn that there are more real numbers than there are integers, but there are just as many pairs of integers as there are integers. In other words, infinity*infinity=infinity whilst 2^infinity>infinity The proofs are pretty easy, but that doesn't make the result less surprising to people who don't know it yet.