**Difference Between Nominal And Ordinal Number**

To a common person who does not hold much knowledge about the subject of mathematics and to him a number is just a mere number. But in reality there exist a lot of differences in different types of numbers in the mathematics subject. Two such numbers are nominal and ordinal numbers and these are very frequently made use of in our day to day lives. The place that a number holds or the position of a particular number in a particular set of numbers is what is called the ordinal number. Thus we can refer to ordinal numbers as the number depicting the relationship between different numbers.A very good example of an ordinary number is the number used to depict the position at which a participant in any particular competition has been placed. In short Ordinal numbers are used to depict any position or rank or space and are used as twenty fourth, third, nineteenth etc. Nominal numbers on the other hand are arbitrary in nature and tend to depict something that has some meaning and need no definition in any set. Nominal numbers are not indicative of any kind of quantity that may include the number of objects, people and other concepts that holds lot of importance in the day to day life. Another good example of nominal number is the Social Security number that all of us make use of. Thus we can draw a conclusion that a nominal number is something that is used to represent anything that holds a lot of importance in our life.

The credit of introducing Ordinal numbers to us goes to Georg Cantor who did it in 1897 so as to provideunlimitedarrangements and also to classify sets indefinitetypes of order assemblies. He shaped a natural number was made use of for two purposes: to depict the size that a set had and also to depict the place that an element holds in a pattern. If we consider the case of nominal numbers, we will see that it was not created by any person and were originally brought into existence for the purpose of being used in text books referred by school children. The origin of the name is from a term used in statistics called “nominal data”. A data which is nominal in nature indicates to the fact that the particular data as well as statements belong to the qualitative class of affiliations. Additionally, nominal numbers find their use in the purpose of identification.The only information provided by this number is the information regarding itself only. It is not necessary that the number is numerical only as it may also consist of alphabets too.

Ordinal numbers may be put to use to perform arithmetic taskssuch as division, addition, subtraction and multiplication. They are able tocreate aclear, well-organizedoutline that can denote a transfinite recursion. Moreover, it may also be usedwhile defining ordinals as done by Von Neumann. As per the definition coined by John von Neumann, ordinal number needs to be in a proper ordered form. Moreover it can also be used in case of transfinite induction which is nothing but awell-organized set that depicts not only the authenticity but also defines the subject matter.

Nominal numbers find their use in the form of an integer too, performing a very important function in depicting the magnitude. Nominal numbers can be used to depict the Zip code of any particular country or region, the driving license number of an individual, the numbers of the National Insurance etc. The numbers that from the telephone numbers etc. are also Nominal Numbers. Even the IP addresses in the IT industries are the Nominal Numbers.

Summary:

1. Ordinal numbers refer to those numbers that depict a particular order or rather the position of a particular number in a definite set of numbers, depicting a date, an object, a place or even a person present in a particular set.

2. The credit of introducing the Ordinal numbers to the human race goes to George Cantor who made use of the same in case of infinite arrangements. Nominal data on the other hand was made to put use to depict a particular data in associations.

3.Ordinal numbers are employed to perform arithmeticprocesses and find their use in our day to day life.