## Calculus 8th Edition

$\displaystyle \lim_{x\rightarrow a}f(x)=L$ if for every number $\epsilon > 0$ there is a number $\delta > 0$ such that the following is valid: $($if $0 < |x-a| < \delta$ then $|f(x)-L| < \epsilon)$ ------------- $f(x)=c$. Given any $\epsilon > 0$, we want to find a $\delta > 0$ such that $0 < |x-a| < \delta\ \ \Rightarrow\ \ |c-c| < \epsilon$. Since $|c-c|=0$, we can take $\delta$ to be any positive number, because the conclusion is always true, regardless of the premise. By the definition, $\displaystyle \lim_{x\rightarrow a}c=c$