I'd say that the problem with transfinites is that you lose intuitive understanding of what's going on, and one of those intuitions is commutativity. People se

I'd say that the problem with transfinites is that you lose intuitive understanding of what's going on, and one of those intuitions is commutativity. People seem to assume that they know a couple of tricks about infinity (adding, multiplying) and don't stop to think that there should be a much more rigorous definition. Which, they shouldn't -- the average person will never _actually_ care about transfinites.