Category:Directed Preorderings

This category contains results about Directed Preorderings.

Let $\struct {S, \precsim}$ be a preordered set.

Then $\struct {S, \precsim}$ is a directed set if and only if every pair of elements of $S$ has an upper bound in $S$:

$\forall x, y \in S: \exists z \in S: x \precsim z$ and $y \precsim z$