The relation
divides
is a partial order: it is reflexive, antisymmetric, and transitive. These properties are expressed in the directed graphs generated here. Reflexivity: there is a path of (zero) arrows from each vertex to itself. Antisymmetry: if there is a path of arrows from
to
, there cannot be a path in the reverse direction. Transitivity: a path of arrows from
to
can be appended to a path of arrows from
to
to create a path from
to
.
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