Greatest element and least element

Hasse diagram of the set $P$ of divisors of 60, partially ordered by the relation "$x$ divides $y$". The red subset $S=\{1,2,3,5,6,10,15,30\}$ has one greatest element, viz. 30, and one least element, viz. 1. These elements are also maximal and minimal elements, respectively, of the red subset.

In mathematics, especially in order theory, the greatest element of a subset $S$ of a partially ordered set (poset) is an element of $S$ that is greater than every other element of $S$. The term least element is defined dually, that is, it is an element of $S$ that is smaller than every other element of $S.$