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

>>25
Who's congo boy?

The trick is not to assosciate with the majority of the maths students socially.

From what I can gather though 90% of the maths students hang out in their own little nerdy clique, and since the top ones don't actually have to work at all, none of the rest do.
I seem to remember in our first year one of the best people spent the entire third term drunk and as a result only got 18 or so alphas (only was his own choice of words, not mine).