if $\displaystyle f(x)=c$ where c is a constant and it is asked to find

$\displaystyle \lim_{x \to a} f(x) = L$

According to the definition we can take

$\displaystyle \forall \epsilon >0 , \exists\delta>0$

$\displaystyle 0<|x-a|<\delta \implies |f(x)-L| < \epsilon$

my question is whether $\displaystyle \delta$ and $\displaystyle \epsilon$ are independent from each other