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

I did the first program on one or two of them. Like prime seives, and euclidean alogrithm for polynomials in a prime field.
From the looks of them they're all pretty self explanitory, but as you say, I'm wary to jump straight in.

Also I'm pretty shit at programing, so I'm gonna wait till I can ask people who know some questions about how to do shit.
As much fun as it is doing it all with basic loops, I tend to lose track of my variables. One of my programs last year was over 1000 lines long. I never could be arsed to write functions.

Then again I read up on galois theory but couldn't make total sense of the program question, differences in notation and stuff. Don't read any book that say's it's going to follow Galois' methods, it's almost unreadable and pretty pointless. Extension fields is where it's at.