Total Order

For a set $X$, elements $a,b,c\in X$

• $a\le a$ (reflexive).
• If $a\le b$ and $b\le c$ then $a\le c$ (transitive).
• If $a\le b$ and $b\le a$ then $a=b$ (antisymmetric).
• $a\le b$ or $b\le a$ (strongly connected, formerly called total).