Well-ordered set

Note: This page exists only to contain a simpler, easier view of Well-ordering - until all the concepts can be united anyway.

Definition

A set $A$ with an linear ordering $<\subseteq A\times A$ where if $(a,b)\in<$ we write $a<b$ is said to be well ordered^[1] if:

That is to say that:

Or more simply:

<cite_references_link_accessibility_label> ↑ Recall that for every linear ordering $>$ there exists a corresponding partial ordering $\ge$ and for every $\ge$ there exists a corresponding $>$