`next`

is monotone for `(L, <=)`

.
The induced union operator $\cup: L \times L \rightarrow L$ is:
$x \cup y \equiv \begin{cases} \texttt{next}(x) & x = y \\ \max(x, y) & x \neq y \end{cases}$

- Is the total ordering on vector clocks
*not*isomorphic to the total ordering on $\mathbb{R}$?