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

>>21

It's not inferiority or superiority, just better at applying to colleges. There's no reasons not to go to trinity anyway, best (and cheapest) rooms, grant money coming out of your arse, One of the largest student bodies, centre of town.....etc.

Maybe I'm confusing him with another professor, but Korner's a dick.

>>19
Not so at all. Maybe you'll pass the exams just as fine, but you'll end up with a shallower understanding of the finer points of the material and it's implications in the wider scheme of things.
Oh and, not sure how true this is for non-pure mathematicians, but in almost all the subjects I revised for the exams this year exam material was written by trinity professors, which is a real help when they're giving you revision supervisions.