# Ordinal Data - Partially Order

### Table of Contents

## 1 - About

A Partially ordered structure is a data structure where not every pair of elements needs to be comparable (compared).

## 2 - Articles Related

## 3 - Example

### 3.1 - Genealogy

A collection of people ordered by genealogical descendancy:

- Some pairs of people bear the descendant-ancestor relationship,
- But other pairs of people are incomparable, with neither being a descendant of the other.

### 3.2 - Heap

A Heap is also a sort of partially ordered structure. (ie the parent node should have a bigger value than the child)

(By Ermishin - Own work, CC BY-SA 3.0)

## 4 - Properties

A partial order is any binary relation that is:

- reflexive (each element is comparable to itself),
- antisymmetric (no two different elements precede each other),
- transitive (the start of a chain of precedence relations must precede the end of the chain).