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} $