ThmDex – An index of mathematical definitions, results, and conjectures.
Nonempty finite poset contains a maximal element
Formulation 0
Let $P = (X, {\preceq})$ be an D1103: Partially ordered set such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $X$ is a D17: Finite set
(iii) $\max P$ is the D4464: Set of maximal elements in $P$
Then \begin{equation} |\max P| \geq 1 \end{equation}