Partially ordered set, maximal and minimal Show there exist partially ordered sers with more than one maximal element and /or more than one minimal element. This is not a Homework question so completeness is appreciated.

Take any set $X$ with more than one element and order $\mathcal {P}(X)\setminus \{\varnothing,X\}$ by inclusion.

The non trivial divisors of any natural composite number which isn't a power of a prime number with the order $a|b\iff (\exists k\in\Bbb N)(b=ak)$, for any $a,b\in \Bbb N$.
