---
tag: V9NXB85SYT
kind: concept
name: Maximal and minimal elements
aliases: [maximal-elements]
sources:
  - wikipedia: en:303398@r1338982942
    locator: Maximal and minimal elements
    note: adopted
    mention: wikipedia://en/303398
    sections: [Summary]
same_as:
  wikidata: Q1475294
  wikipedia: Maximal and minimal elements
inventory: [TJ67AQG0A6]
---

## Summary

In mathematics, especially in order theory, a **maximal element** of a [[subset|0BJR9QR08E]] $S$ of some preordered set is an element of $S$ that is not smaller than any other element in $S$. A **minimal element** of a subset $S$ of some preordered set is defined dually as an element of $S$ that is not greater than any other element in $S$.