\begin{definition}[Definition:Maximal Chain]
Let $\left({S, \preceq}\right)$ be an ordered set.
Let $\left({T, \preceq}\right) \subseteq \left({S, \preceq}\right)$ be a chain in $\left({S, \preceq}\right)$ such that there is no other chain in $\left({S, \preceq}\right)$ which has $\left({T, \preceq}\right)$ as a proper subset.
Then $\left({T, \preceq}\right)$ is a '''maximal chain in $S$'''.
Category:Definitions/Order Theory
\end{definition}