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

>>17
Big deal. I'm sure whatever the staff, regardless of their fame, they at least understand undergraduate material just fine. Does a PhD in maths teach GCSE/A level maths any better than someone with just a masters? No.

I couldn't give a shit about my peers or their aptitude either.

Sounds like you're just have a superiority complex.