If $≤$ is a total ordering on A, then every non-empty finite subset S of A has a least element and a greatest element.
I was wondering whether this result is true if we replace "total ordering" by partial ordering.
Do we have some example. Thanks for help and reading out.
Not true in general for partial order.
Counterexample: set $A$ with more than one element and equipped with partial order $=$.
If $a,b\in A$ with $a\neq b$ then the set $\{a,b\}$ has no least and no greatest element.