1. The problem statement, all variables and given/known data Let f, g : D→R be uniformly continuous. Prove that f-g: D→R is uniformly continuous aswell 2. Relevant equations none 3. The attempt at a solution Okay, I am posting this question because I want to make sure that my solution is correct and if it isn't I would really be thankful if someone pointed out its flaws. My solution: For all ε >0 there exists δ >0 s.t. abs( x - y ) < δ => abs( f(x) - f(y)) <ε then abs( f(x) - f(y)) <ε/2 abs( g(x) - g(y)) <ε/2 now its f - g so abs( f(x) - f(y) - g(x) + g(y)) < ε abs( f(x) - f(y)) + abs( - g(x) + g(y)) < ε abs( f(x) - f(y)) + abs(-1)*abs( +g(x) -g(y)) < ε abs( f(x) - f(y)) + abs( +g(x) -g(y)) < ε ε/2 + ε/2 <ε ε ≤ ε Also can anyone describe to me what uniformly continuous means besides from the actual definition. I have a hard time understanding what uniformly continuous means. Thanks.