Limit

The precise definition of a limit:
Suppose $f:X\to \mathbb{R}$ is a function where $X\subseteq \mathbb{R}$, and $c\in \mathbb{R}$. Then ${\lim }_{x\to c}f(x)=L$ means that for any real $ϵ>0$ (no matter how small), there is a real number $\delta >0$ for which $|f(x)-L|<ϵ$ provided that $0<|x-c|<\delta$.