1. The problem statement, all variables and given/known data Prove that if f is continuous at a, then for any ε>0 there is a σ>0,? such that if abs(x-a)< σ and abs(y-a)< σ then abs[f(x) - f(y)]< ε 2. Relevant equations Definition of continuity and triangle inequality abs(f(x)-f(y))= abs(f(x)-f(a) + f(a)-f(y))≤ abs(f(x)-f(a))+ abs(f(y)-f(a)) 3. The attempt at a solution So i think I need to apply the continuity definition twice and bring things together with the triangle inequality but i don't know how to go about it all.