if X is a function from metric space X to Y and x is an element of X, i need to show that the definition of continuity given by (for each open neighborhood V of f(x), there exists an open neighborhood U of x s.t. f(U) is a proper subset of V) coincides with the definition given by (whenever {X_n} is a sequence in X s.t. x_n converges to x, then f(x_n) converges to f(x)).
i can't seem to relate the two definitions too well. help?