Category:Directed Orderings

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This category contains results about Directed Orderings.

Let $\struct {S, \preccurlyeq}$ be an ordered set.

Let $\struct {S, \preccurlyeq}$ be such that:

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

That is, such that every pair of elements of $S$ has an upper bound in $S$.

Then $\preccurlyeq$ is a directed ordering.