---
tag: M3VR2FMG97
kind: concept
name: Greatest element and least element
aliases: [bottom-element, greatest-and-least-elements, largest-element, largest-member, least-and-greatest-elements, lowest-element, top-element]
sources:
  - wikipedia: en:663041@r1320031333
    locator: Greatest element and least element
    note: adopted
    mention: wikipedia://en/663041
    sections: [Summary]
same_as:
  wikidata: Q1196892
  wikipedia: Greatest element and least element
inventory: [8PBMB3RTGB]
---

## Summary

In mathematics, especially in order theory, the **greatest element** of a subset $S$ of a [[partially ordered set|0QV2JS9RJ3]] (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 $S.$