Thread: Real Analysis limit proof

Suppose f: D---> R, g:E--->R, x_0 is an accumulation pt of D intersect E and there is epsilon>0 such that D interesect [x_0 - epsilon, x_0 + epsilon]= E intersect [x_0 - epsilon, x_0 + epsilon]. If f(x0=g(x) for all x element of D intersect E intersect [x_0 - epsilon, x_0 + epsilon], prove that f has a limit at x_0 iff g has a limit at x_0.

I'm clueless.....

Originally Posted by kathrynmath

Suppose f: D---> R, g:E--->R, x_0 is an accumulation pt of D intersect E and there is epsilon>0 such that D interesect [x_0 - epsilon, x_0 + epsilon]= E intersect [x_0 - epsilon, x_0 + epsilon]. If f(x0=g(x) for all x element of D intersect E intersect [x_0 - epsilon, x_0 + epsilon], prove that f has a limit at x_0 iff g has a limit at x_0.

I'm clueless.....

I'm just not quite sure what this problem is saying?