Definition:Local Minimum in Set of Reals

Definition
Let $X$ be a subset of $\R$, the set of all real numbers.

Let $x$ be a real number, $x \in \R$.

$x$ is local minimum in set $X$


 * $x \in X \land \exists y \in \R: y < x \land \left({y \,.\,.\, x}\right) \cap X = \varnothing$