Some [[Set]] $O$ is [[Convex]] [[Biconditional|if and only if]] [[Universal Quantifier|for any]] two [[Point|points]] $p_{0},p_{1} \in O$, the [[Line Segment]] connecting $p_0$ and $p_{1}$ is entirely contained within $O$.
In simplified terms, a [[Convex]] shape is one that 'bulges out' / does not cave in. If $O$ is not [[Convex]], then it is [[Concave]].
$\huge
\begin{align}
\forall p_{0},p_{1} &\in O\\
\overline{p_{0}p_{1}} &\subseteq O
\end{align} $