What is the point of exercises for which answers aren't provided? (That is to say, what is the pedagogical justification for such exercises? - Edit by someone other than original poster.)
Commentary behind the question by original poster:
Most if not all courses I've taken, math or otherwise, come with books with exercises where answers aren't always provided. What are students supposed to learn from such exercises?
I'm not necessarily talking about "difficult" exercises here. Indeed it's even worse when "exercise 1" doesn't come with an answer - the student has no way of confirming that he understood even that first paragraph of the entire book.
If you don't know how to solve something right away then you need the answer to guide you. The activity of trying and trying until you're completely exhausted and just have to give up, need not be fruitful, the approaches you tried may have been way off.
Yes, providing answers may cause some students to not bother taking the time to try on their own, but that's their responsibility.