Companions of directed sets and the Ordering Lemma Given a partially ordered set $(D,\leq)$, a companion $(C\preceq)$ of $(D,\leq)$ is a well ordered set where $C$ is a cofinal subsets of $(D,\leq)$ such that for every $c_1,c_2\in C$ if $c_1\leq c_2$ then $c_1\preceq c_2$. The Ordering Lemma says that every partially ordered set has a companion. Given a directed set $(D,\leq)$ and a net $f:D\rightarrow X$, the restriction $f\upharpoonright C$ of the net to the companion $(C,\preceq)$ of $(D,\leq)$ is a transfinite sequence. We show how the convergence and clustering of $f\upharpoonright C$ is related to the convergence and clustering of $f$.