A [[Set]] $O$ is [[Concave]] [[Biconditional|if and only if]] there [[Existential Quantifier|exists]] two [[Point|points]] $p_{0},p_{1}\in O$ who form a [[Line Segment]] that is not entirely contained in $O$.
$\huge
\begin{align}
\exists p_{0},p_{1}&\in O\\
\overline{p_{0}p_{1}} &\nsubseteq O
\end{align} $