On this page there are some examples of directed sets. One of those cites:
"If $x_0$ is a real number, we can turn the set $\mathbb{R} − \{x_0\}$ into a directed set by writing $a \leq b$ if and only if $|a − x_0| \geq |b − x_0|$. We then say that the reals have been directed towards $x_0$. This is an example of a directed set that is not ordered (neither totally nor partially)."
Can you show me why such a set is not partially ordered?