Originally Posted by

**pberardi** I think I have the idea but I am having trouble finishing off these. Can I just post the questions and my attempt at the solutions hoping that someone can explain how to finish or if I am right? Thanks.

#2

Let x, y be in R(real #s) with x != y. Prove that there is a neighborhood U and a neighborhood V s.t. the intersection of U and V is the empty set. i.e. U and V are disjoint sets.

#2 Solution attempt

Here I just pick E to be 1

Therefore x-1<x<x+1 and y-1<y<y+1

or: (x-1,x+1) is U and (y-1,y+1) is V

so |x| < 1 and |y| < 1. I thought I had it because I thought the the only way this could be true is if x = y. But then what if x was 1/2 and y was -1/2, this could still hold. So I thought maybe I am not thinking right.

Any help on these two?