---
tag: PW2NKAPXWA
kind: concept
name: Weak ordering
msc: [06A06, 06A05]
specializes: [60FNZ35H6R]
sources:
  - url: https://en.wikipedia.org/wiki/Weak_ordering
same_as:
  wikidata: Q1414271
  wikipedia: Weak ordering
---

## Summary

A weak ordering ranks the elements of a set where ties are allowed.
In its strict form it is a [[strict partial order|SWB1ZXFVKY]] in which incomparability is transitive.
Then the elements fall into classes of tied elements, and these classes are totally ordered.
Weak orderings model rankings with ties, such as the results of a race with shared places.

## Explanations

### L1 human

Think of the final ranking of a competition where several people can share a place.
Each person is strictly ahead of, strictly behind, or tied with each other person.
If Ann and Bob are tied and Bob and Cem are tied, then Ann and Cem are tied too.
For example, sorting people by age in whole years gives a weak ordering: "is younger than" in whole years, with people of the same age tied.