Just to get a feel for surjections, I'm trying to think of some surjections from uncountable sets to countable sets. For R to N, I thought of using what I found out is called the ceiling function, but I can't think of any others. So, for instance, for the set of reals 0 < r < 1 to N, I can't think of any. Does anyone know of some examples? BTW, I'll try to figure out next if it holds in general that if A is uncountable and B is countable, there exists a surjection from A to B, so if you can help it, please don't give me a proof :) Thanks.