The **well ordering property** of $\mathbb{N}$, the [[Natural Number|natural numbers]], says that all [[‡ nonempty]] [[Subset|subsets]] of $\mathbb{N}$ have a *least* or *smallest* [[Element of a Set|element]]. $\exists x\in S \mid x\leq y \quad \forall y\in S$ $\set{\ldots,y_6,y_4,{\color{orange}{x}},y_1,y_2,\ldots}$