I am wondering how to prove that the intersection of an infinite number of convex sets is convex.
I can prove that the intersection of two convex sets is convex, and I believe that I can simply do an induction on this result, but I've heard that it would be wrong to do this since I am working with infinity.
I guess another way to think of this question is whether or not I have to take something special into consideration since the word "infinite" is involved.