# Thread: determining epsilons and deltas

1. ## determining epsilons and deltas

How do you find appropriate values for epsilon and delta's to use in proofs of continuity. I know delta depends on epsilon.

2. ## Re: determining epsilons and deltas

Continuity states that for every $\epsilon > 0$, there exists a $\delta > 0$ such that $|x - x_{0}| < \delta \implies |f(x) - f(x_{0})| < \epsilon$. So we pick an arbitrary $\epsilon$. That is, we simply say: Let $\epsilon > 0$, then we solve for $\delta$.