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

>>36
It started off with a question about the logarithm, which may have turned you off, but it just asked you to suitably define the logarithm the map C - { (0,-inf] } to some slice of the complex plane.

Yeah, ben green was that guy, he proved that their are arbitrarily long arithmetic sequences of primes amongst other things. Nice guy as well.

Compared to past papers I did abysmally. Somehow I even managed to mess up that question that was literally "Prove all norms are equivalent in R^n", and I still have no idea how. CATAM was an easy 4 alphas though.

I should have spent the time to learn something bankable like optimization or Markov chains, but fuck it, it's this year that counts.

You staying on for part III?