\begin{definition}[Definition:Concave Real Function/Definition 1/Strictly]
Let $f$ be a real function which is defined on a real interval $I$.
$f$ is '''strictly concave on $I$''' {{iff}}:
:$\forall x, y \in I, x \ne y: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: f \left({\alpha x + \beta y}\right) > \alpha f \left({x}\right) + \beta f \left({y}\right)$
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The geometric interpretation is that any point on the chord drawn on the graph of any '''strictly concave function''' always lies below the graph.
\end{definition}