I have been told that a function $f$ is continuous at $c$ if for every $\epsilon >0 $ there exists a $ \delta >0 $ such that:
$|x-c|<\delta \Rightarrow |f(x)-f(c)|< \epsilon$
This may be a stupid question, but is this the same as saying $f$ is continuous at $c$ if for every $\delta >0 $ there exists an $ \epsilon >0 $ such that:
$|f(x)-f(c)|< \epsilon \Rightarrow |x-c|<\delta$ ?
Thank you in advance.