Continuity

In layman’s terms, when a Function can be drawn without “picking up the pen”.

$$\begin{array}{c}f\text{ is continuous}\\ ⟺\\ \forall ϵ>0,\exists \delta >0\\ \text{ s.t. }\forall x\in D\\ |x-d|<\delta ⟹|f(x)-f(d)|<ϵ\\ \text{for}f:D\to C,d\in D\end{array}$$

• where $D$ is the Domain of the function
• where $C$ is the Codomain of the function