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

>>39

I've already bought Stewart's =[ I'm making my way through but it's annoying having to skim sections - on stuff anyone that reads it should already know - in case he introduces a method or notation that I haven't seen before.

How can you not be arsed to write functions, but be prepared to go through the trauma of recalling which variable does what, presumably write similar loops over and over and have to face a monumental pile of compiling errors?