Epsilon-Delta Definintion of Continuity

[onemachine]

Here is the definition:

A function f is continuous at a point c if
given epsilon > 0, there exists delta > 0 such that if |x-c| < delta, then |f(x)-f(c)| < epsilon.

Is this actually an if and only if definition?

That is, does "for all epsilon > 0, there exists delta > 0 such that if |x-c| < delta, then |f(x)-f(c)| < epsilon" imply that f is continuous at c?

Thanks for your help!

 

[onemachine]

Yes, if and only if. Note that this definition implies that f(c) exists.

Sweet, thanks! I had to make sure because every definition I can find does not use "iff" or "provided", they are all of the form "if, then".