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

I've been supervised by the guy who SUPERVISED Tim Gowers. Wayne Boucher the legend XD. He said that Cowers wasn't too bright when he was taking him, lol.

Anyway, yeah you do have a bit of an inferiority complex (>>19 had it the wrong way round). Though the best students tend to be at Trinity (bar e.g. one guy in my year, Clare), on average the people you work with will be roughly the same at any college.

>>14
I heard once that Korner is DoS at Tit Hall and you don't have to do example sheets in the first year. Nice choice.