Compare the Difference Between Similar Terms

Difference Between

Home / Science & Nature / Science / Mathematics / Difference Between Cardinal Numbers and Ordinal Numbers

Difference Between Cardinal Numbers and Ordinal Numbers

February 20, 2013 Posted by Admin

Cardinal vs Ordinal 
 

In our day to day life, the use of numbers may take different forms in different situations. For example, when we count to figure out the size of a collection of objects, we count them as one, two, three, and so on. When we want to count something to get the sense of the position of the objects, we count them as first, second, third, and so on. In the first form of counting, numbers are said to be cardinal numbers. In the second form of counting, the numbers are considered as ordinal numbers. In this context, the concepts cardinal and ordinal are completely a matter of linguistics; cardinal and ordinal are adjectives.

However, the extension of the concept to sets in mathematics reveals a much deeper and broader perspective and cannot be treated in simple terms. In this article, we will try to understand the fundamental concepts of cardinal and ordinal numbers in mathematics.

Formal definitions of cardinal and ordinal numbers are provided in the set theory. The definitions are intricate and to understand them in perfect sense needs background knowledge in set theory. Therefore, we will turn towards a couple of examples, to understand the concepts heuristically.

Consider the two sets {1,3,6,4,5,2} and {bus, car, ferry, train, airplane, helicopter}. Each set lists a set of elements, and if we count the number of elements it is evident that each has the same number of elements, which is 6. Arriving at this conclusion we have taken the size of one set and compared to another using a number. Such a number is called a cardinal number. Therefore, we can say that a cardinal number is a number we can use to compare the size of the finite sets.

Again the first set of numbers can be arranged in ascending order considering the size of each element and comparing them. In the process of ordering, the numbers are considered as cardinals. Likewise, the set of all nonnegative integers can be ordered in a set; i.e {0,1,2,3,4,…..}. But in this case, the size of the set becomes infinite, and giving it in terms of ordinals is not possible. No matter how large a number you pick to give the size of the set, still there will be numbers left out of the set you pick and which are nonnegative integers.

Therefore, mathematicians define this infinite cardinal (which is the first) as Aleph-0, written as א (first letter in the Hebrew alphabet). Formally the ordinal number is the order type of a well ordered set. Therefore, the ordinal number of the finite sets can be given by cardinal numbers, but for infinite sets ordinal is given by transfinite numbers such as Aleph-0.

What is the difference between Cardinal and Ordinal Numbers?

• The cardinal number is a number that can be used to count, or to give the size of a finite ordered set. All cardinal numbers are ordinals.

• The ordinal numbers are numbers used to give the size of both finite and infinite ordered sets. The size of the finite ordered sets is given by usual Hindu-Arabic algebraic numerals, and the infinite set size is given by transfinite numbers.

Related posts:

Difference Between Nominal and Ordinal Difference Between Ordinal Data and Interval Data Difference Between Discrete and Continuous Variables Difference Between Definite and Indefinite Integrals Difference Between Variable and Random Variable

Filed Under: Mathematics Tagged With: Cardinal, Cardinal Numbers, Cardinal Numerals, Ordinal, ordinal numbers, Ordinal Numerals

About the Author: Admin

Coming from Engineering cum Human Resource Development background, has over 10 years experience in content developmet and management.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Request Article

Featured Posts

Difference Between Coronavirus and Cold Symptoms

Difference Between Coronavirus and Cold Symptoms

Difference Between Coronavirus and SARS

Difference Between Coronavirus and SARS

Difference Between Coronavirus and Influenza

Difference Between Coronavirus and Influenza

Difference Between Coronavirus and Covid 19

Difference Between Coronavirus and Covid 19

You May Like

Difference Between Bermuda Grass and St. Augustine Grass

Difference Between Hydrogen Bond and Ionic Bond

Difference Between Hydrogen Bond and Ionic Bond

Difference Between Ranger and Green Beret

Difference Between Ranger and Green Beret

Difference Between Snuggle and Cuddle

Difference Between Chiral and Achiral

Latest Posts

  • What is the Difference Between Squalane and Hemi-squalane
  • What is the Difference Between Anencephaly and Microcephaly
  • What is the Difference Between Neuroleptic Malignant Syndrome and Serotonin Syndrome
  • What is the Difference Between Resolutions and Goals
  • What is Difference Between Tay-Sachs Disease and Niemann-Pick Disease
  • What is the Difference Between Enucleation and Marsupialization
  • Home
  • Vacancies
  • About
  • Request Article
  • Contact Us

Copyright © 2010-2018 Difference Between. All rights reserved. Terms of Use and Privacy Policy: Legal.