Ordinal Numbers: Facts About Them

A natural number (including 0 in this context) can be used for two purposes: to describe the size of set as well as describing the position of elements of a set. This article is about describing some important facts for the number of words denoting a position in a sequence. Any finite collection of objects can be arranged in order merely by the process of counting.  Ordinal number forms a part of set theory. This is a generalized concept used to describe a way to arrange a collection of objects in order, one after another. The basic idea of ordinal numbers is the process of generalization of labels needed to arrange collections in perfect order.

When ordinal numbers are used for ordering sets they form a different representation as compared to cardinal numbers. Cardinal numbers are used for quantifying data whereas ordinal numbers are for positioning data. The notion of cardinal numbers is not associated with any particular structure but ordinals are intimately linked with a special kind of well-ordered sets.

Definition: An ordinal number is genuinely an equivalence class of well-ordered sets. It can also be defined as well-ordered sets that represent a class which is a subset of real number.

Ordinal arithmetic

There are three usual operations on ordinals: addition, multiplication, and exponentiation.

Meaning of ordinals

  1. A number designated the place occupied by an item in an ordered sequence, such as, first, second, third, etc.
  2. A number assigned to an ordered set that designates both the order of its elements and its cardinal numbers.

Difference between cardinal and ordinal numbers

Cardinal numbers tell ‘how man’, i.e. quantity of something while ordinal numbers tell the rank or position of the elements of a set.

Each ordinal number is associated with cardinal numbers, its cardinality. Ordinal numbers can be used conveniently in a sentence as they help to put the things according to the rank of the elements.

Ordinal numbers are mostly written as words, especially in formal writing. Letters at the end of an ordinal numeral are often written in superscript.

Purpose of usage: The purpose of these ordinal numbers is to indicate position or order of things or objects. Ordinal numbers are commonly used in mathematics, sciences, literature, and each and every aspect of life. The main function is to arrange different things in order due to the position and status of things.

List of ordinal numbers:  Here is a list of some ordinal numbers.

Ordinal Numbers 1 to 50

1st: First

11th: Eleventh

21st: Twenty-First

31st: Thirty-First

41st: Forty-First

2nd: Second

12th: Twelfth

22nd: Twenty-Second

32nd: Thirty-Second

42nd: Forty-Second

3rd: Third

13th: Thirteenth

23rd: Twenty-Third

33rd: Thirty-Third

43rd: Forty-Third

4th: Fourth

14th: Fourteenth

24th: Twenty-Fourth

34th: Thirty-Fourth

44th: Forty-Fourth

5th: Fifth

15th: Fifteenth

25th: Twenty-Fifth

35th: Thirty-Fifth

45th: Forty-Fifth

6th: Sixth

16th: Sixteenth

26th: Twenty-Sixth

36th: Thirty-Sixth

46th: Forty-Sixth

7th: Seventh

17th: Seventeenth

27th: Twenty-Seventh

37th: Thirty-Seventh

47th: Forty-Seventh

8th: Eighth

18th: Eighteenth

28th: Twenty-Eighth

38th: Thirty-Eighth

48th: Forty-Eighth

9th: Ninth

19th: Nineteenth

29th: Twenty-Ninth

39th: Thirty-Ninth

49th: Forty-Ninth

10th: Tenth

20th: Twentieth

30th: Thirtieth

40th: Fortieth

50th: Fiftieth

Here are a few guidelines for determining which suffix to add to a number.

  1. The ordinal for the numbers that end in 1 has –st as the suffix.
  2. The ordinal for the numbers that end in 2 has –nd at the end.
  3. The ordinal for the numbers that end in 3 has –rd at the end.
  4. When a number ends in 0, 4, 5, 6, 7, 8 or 9 uses –th as a suffix.
  5. An exception to the rules above is 11, 12, 13 which use –th as suffix.

The simple rules and the list above make it simple to understand the concept of ordinal numbers and can help to turn a cardinal number to an ordinal. Both the cardinal numbers and ordinal numbers come from a set of real numbers and are explained by Cuemath in an efficient way.


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