email@example.com wrote in message <firstname.lastname@example.org>... >Theorem >Prove if is A dense in X and x(-X then every neighborhood of x inter- >sects A. > >Proof(kind of) > >Given a set X .C. R ,the set A .C. X is dense in X if every >point of X is a limit point of A or it is a point of A , >where '.C.' =subset of > >Let a(-A and be an isolated point of A. Then a(-A has a neighborhood >which contains no other points in A. Since A .C. X and A is dense in X >then a(-X.But x(-X in the neighboorhood of A. Then I guess it >intersects A?
I think you started this paragraph off wrong. You should say, "Let x(-X and U be a neighborhood of x." Then see what happens if U does not intersect A in order to show that it must, which would prove the theorem.