- An element in is called
*a maximal element*in if there exist no such that . - An element in is called
*a minimal element*in if there exist no such that .

- An element is the greatest element of if, for any element , we have .
- An element is the least element of if, for any element , we have .

- The set has a least element (namely ) and a greatest element (namely ).
- The poset , ordered by division, has neither a least nor a greatest element.
- The poset , ordered by division, has as its least element and has no greatest element.