\begin{definition}[Definition:Convex Subset of Natural Numbers]
Let $A \subseteq \N$ be a subset of the set of natural numbers.
$A$ is defined as being '''convex (in $\N$)''' {{iff}}:
:$\forall x, y, z \in \N: \paren {x, z \in A \land x \le y \le z} \implies y \in A$
\end{definition}