Epsilon-delta definition of a limit ($\forall \epsilon >0\exists \delta >0:0<|x-a|<\delta \Rightarrow |f(x)-L|<\epsilon$)

The assertion $f(x)\to L$ as $x\to a$ means that for every $\epsilon >0$ there is $\delta >0$ such that $0<|x-a|<\delta$ implies $|f(x)-L|<\epsilon$.