strict total order

A strict total order is a homogeneous relation that is irreflexive, antisymmetric, transitive, and connected.

Formally,
a binary relation $<$ over a set $S$ is a strict total order if for all $a,b,c$ in $S$,

• $a\nless a$ (irreflexive)
• if $a<b$ and $b<c$ then $a<c$ (transitive)
• if $a<b$ then $b\nless a$ (antisymmetric)
• either $a<b$ or $b<a$ (connected)

A strict total order is a strict partial order that is connected.