Continuity
Definition
A function $f:A \rightarrow \mathbb{R}$ is continuous at a point $c \in A$, for all $\epsilon > 0$, there exists a $\delta > 0$ such that whenever $|x - c| < \delta$ and (and $x \in A$), it follows that $\left| f\left. (x) \right. - f\left. (c) \right. \right| < \epsilon$.
If $f$ is continuous at every point in the domain $A$, then we say that $f$ is continuous on $A$.