The book "Selected Problems in Real Analysis" was recommended in this article:
For those of you who don't know the book: It is a book that only consists of mathematical problems, starting from problems about set theorie and ending with problems about measure theorie. It seems to be rather challenging. I already attended Analysis I and Analysis II, currently I'm hearing Analysis III.
Now, I'm wondering how to start with a book like this. He merely gives a background about the questions he asks, which means that there might be tasks where I simply don't have a good foundation. For example, the first task is to prove that the power set of $\Bbb N$ and the set of all possible binary sequences have the same cardinality.
Assuming that I didn't have any clue about what he is talking there (which is not true in this case, but there might be cases like this), how would one approach a problem like this?
Normally, one has the foundation given by the lectures, but that kind of style is completely different of course.