\begin{definition}[Definition:Local Minimum in Set of Reals]
Let $X$ be a subset of $\R$, the set of all real numbers.
Let $x \in X$.
Then $x$ is '''local minimum in set''' $X$ {{iff}}:
:$\exists y \in \R: y < x \land \openint y x \cap X = \O$
\end{definition}