The term
strict refers to the requirement
of an irreflexive relation (
!comp(x, x) for all
x),
and the term
weak to requirements
that are not as strong as those for a total ordering,
but stronger than those for a partial ordering
. If we define equiv(a, b) as !comp(a, b) && !comp(b, a),
then the requirements are that comp and equiv
both be transitive relations: