Difference Between Nominal and Ordinal Number

Nominal vs Ordinal Number

A number isn’t just a number contrary to the popular perception of men. There’s actually more to it because it is fascinating and diverse. As a matter of fact, it can be categorized into ordinal and nominal numbers. Without knowing, such numbers are used in our daily lives. An ordinal number would pertain to the place or order of a number in a given set. It is safe to conclude that ordinal numbers are relational. A good example would be the placement of an athlete in a competition. You will have to use an ordinal number for that.

Basically, ordinal numbers indicate the rank, space, and position. You can actually use words to represent numbers. “First, second, third, tenth, sixty-ninth” are some of the lexical examples of ordinal numbers. You can even make use of ordinal numbers in your age. Say, for example, you are 20. It would be appropriate for you to say that you are in your 20th year. As for nominal numbers, they are arbitrary. Most of the time they represent something that is meaningful. It doesn’t have to be defined within a set. Also, they don’t represent any quantity. You will be using numbers to represent persons, concepts, objects which are vital in everyday life. A good representation would be your Social Security number which is used by many individuals. It could also be the number on the jersey uniform of a famous soccer player. It is safe to say that nominal numbers are any numbers that represent something important.

Ordinal numbers were introduced by a man named Georg Cantor in the year 1897. He created these numbers so he can cater infinite sequences and to categorize sets with certain kinds of order structures. He created a natural number which can be used for two things: to describe the size of a set and to describe a position of an element in a pattern.

As for nominal numbers, there was no certain person responsible for the creation of them. However, they were originally created to be used in school textbooks. It was derived from the statistical term called “nominal data.” Nominal data would mean indicating data and statements of a qualitative category of memberships. In mathematical terms, the use of nominal numbers is a one-to-one function that originates from a set of items being coined to the set of numerals. Furthermore, nominal numbers are numbers for assigned identification. It is a number with no other information except for the identification itself. Primarily, it was used to name objects, but it doesn’t necessarily consist of numbers alone. It can be alphanumeric.

Ordinal numbers can be used in arithmetic operations like addition, multiplication, subtraction, and division. They can construct an explicit, well-ordered pattern that can represent a transfinite recursion. In addition, it can be used in the definition of ordinals by von Neumann. According to the standard definition made by John von Neumann, an ordinal has to be well ordered from a set of all smaller ordinals. What is more is that it can be used in transfinite induction. Transfinite induction refers to the well-ordered set that won’t only prove things but would also define things.

Nominal numbers can be used as an integer,playing a vital role in magnitude. You could use nominal numbers in a ZIP code. Also, you can use nominal numbers in driver’s license numbers and registrations and the National Insurance number. That’s not all, it could also be routing numbers, telephone numbers, bank codes, sort codes like IBAN, and the ABA routing transit numbers are some good examples. Lastly, they are also used in computer applications like the IP addresses and in some international policies.

Summary:

1. Ordinal numbers are numbers that refer to an order or place of a number in a given set. Nominal numbers are numbers that represent an object, person, date, or place within a set.
2.Ordinal numbers were introduced by Georg Cantor used in infinite sequences. Nominal data were not introduced specifically but initially wereused to indicate data in memberships.
3.Ordinal numbers can be used in arithmetic operations. Nominal numbers are found in everyday life.

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