Basic sets

I'm having problems with questions g) and k).

For g), apparantly the answer is i) but it seems to me they're all the same.If |b'| is a finite subset of an infinite set, then |b| must be an infinite set as N is infinite. Is there any difference between saying "b is infinite" and "|b| = infinity"?

For k), apparantly the answer is i) as well, but I still don't understand the notation. Could someone explain it through?.

Page in question: http://i38.tinypic.com/142ev41.jpg

>>16

Which college you're in?

Yeah. For example at trinity you get supervised by trinity fellows and grad students. Our fellows and grad students are much better than your fellows and grad students.

For example I've been supervised by people like Ben Green, Imre leader, tim gowers.

Also it's self perpetuating. All the mathematicians at trinity are better, so you learn more from your peers (Although don't hand around with maths students, they're autistic).