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

>>33
Combinatorics, cool. He seems like that sort - innovative and new thinking on simple-looking concepts like Leader et al.

I agree that pure was quite hard, thank fuck I internalised some standard Quantum and Markov techniques. I don't remember there being an easy conformal mapping of the kind they've been having for the past four or five years though...