# Greatest element and least element

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