What Is a Natural Number

Ordinary whole numbers used in every day counting are referred to as natural numbers in the field of mathematics. An example here is 6 pieces of bread. 6 here is a whole number as opposed to ½ a bread where ½ is not a whole number. Whole numbers are also used for giving orders to numbers. The purposes related to these numbers originate from English numerals which are used in English speaking cultures. But there are also nominal numbers which are only used for grouping things. Nominal numbers are only used for grouping things and are very limited in use. Examples of nominal numbers include social security numbers and driver’s license numbers.

The properties of natural numbers relate to divisibility and the distribution of prime numbers as studied in the number theory. However other theories such a partitioning enumeration are studied under a different branch of mathematics known as combinatorics. There is no universal consensus as to whether zero should be included in the natural numbers set. One group defines natural numbers as a set of integers, starting from 1, 2, and 3 and so on while another group believes that non-negative integers form the natural numbers sequence, starting from 0, 1, 2, and 3 and so on. Positive integers forms the traditional school of thinking while non–negative integers is a much later group which first appeared in the 29th century. Therefore you will find that some people use natural numbers so as to exclude zero while other people use the term to include zero.

The history of natural numbers lies in the establishment of a system of counting things, with number 1 being the start point. Major advancement in the field of natural numbers came after the introduction of numerals to characterize numbers. Egyptians came up with a very advanced system where 1 and 10 were clearly differentiated with distinct hieroglyphs. Further advancement came through a development of an idea that zero could be considered as a number. The use of zero or its placement in other numbers dates back to 700BC in ancient Babylon.

There are two generalizations accepted when it comes to natural numbers. One of these generalizations states that natural numbers are used to show the size of finite amount of objects. Cardinal numbers generally are used to measure the size of a set of infinite objects. The other generalization comes in the form of linguistic ordinal numbers. ‘First’, ‘second’, ‘third’ etc are assigned to the total of finite set of objects. It can also be used to order infinite object. In short this generalization is used to assign the position of elements within a group. But as shown above, natural numbers can be assigned to both finite and infinite objects.

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