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

>>22
| There's no reasons not to go to trinity anyway

I can think of a couple. You get not only the people who are amazing at maths, but also the people who *think* they're amazing. I.e. the massive nobs. I got a good first this last year, which has put me above a good number of Trinity students (including Congo boy lol), all without having to suffer the smarmy arrogance of people I've known from my school who've gone to Trinity.

Also, I hear the work ethic is pretty heavy; I know people probably do varying amounts but it seems like a lot of Trin students work themselves skinless in the third term. I don't want that kind of pressure, doesn't work for me.