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Mathematics is a complicated and fascinating subject. Everyone who has been to school has studied this particular subject for a very long period of time. The reason behind this is the demand for this subject in everyday life. Calculations surround the life of a person in such a way that it feels like salt in food. Its presence is not that intimidating, but if it’s not there, nothing else will make sense.
Mathematics has many sections and components, but its core lies in numbers. The combination of digits follows every person wherever they go and whatever they think of. Numbers are part of life so much so that they are used more than people think they do. This article is going to focus on numbers, and one of its popular kinds is natural numbers.
Numbers
Numbers are known as the combination of digits that are used for various mathematical purposes. The most common use of these terms is calculation. When a person thinks of numbers, there is a certain kind of symbol that comes to their mind, which is either one or multiple, depending on the number they are thinking of. These symbols are digits that are different in every language and are called numerals. In order to understand this, it is important to understand both the terms.
Digits are the components that form numbers. There are ten digits that combine with each other to form different numbers. The ten digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The reason behind having ten digits is the lack of retention power of people. If there were a different digit for every number, then it would become a complex task to understand numbers, and nobody would be able to remember every digit. There are various kinds of numbers depending upon various criteria. The discussion, for now, is going to be restricted to natural numbers and number lines.
Natural Numbers
There are different kinds of numbers, but the most primitive form and type of numbers are the natural numbers which can be defined as the positive integers starting from 1. There are various perspectives on a particular type of number because of its ancient origin. It took a lot of time to discover negative and irrational numbers as well as the concept of infinity. The most basic kind of number is counting numbers which form natural numbers. Every other number is not a part of everyday mathematics activities and was discovered by various mathematicians for different purposes.
There is a controversy, or one can say a difference of perspective among people regarding the inclusivity of zero in natural numbers. Zero was discovered by Indian mathematician Aryabhatta, and later on, people started considering it as part of natural numbers, but as per the modern definition and the way numbers are differentiated, 0 included with natural numbers forms whole numbers.
Natural numbers are the most basic form of numbers that are most commonly used by people, and there have been a lot of definitions for me. Many mathematicians defined natural numbers and researched a lot about them in India, China and Greece. People even claimed that natural numbers are a direct creation of God, and a notable mathematician named Frege also defined natural numbers but had a lot of contradictions attached to them. As of today, natural numbers are 1 to infinity.
Properties of Natural Numbers
Natural numbers are the simplest form of numbers and can be easily understood because they are a part of common life. People often keep adding, subtracting, dividing and multiplying these numbers without having a conscious realisation about the same. The properties of natural numbers in various mathematical operations are discussed below.
Addition– During the process of addition, when one natural number is added with another natural number, the result will always be a natural number and nothing else. This is known as closure property and can be better retained through a simple example given.
For Example, 8(natural number) + 24 (natural number) = 30(natural number)
Another property which is applicable in case of natural numbers is that a+b = b+a
Multiplication– When two natural numbers are multiplied, the product is a natural number without any contradiction.
Example– 4(natural number) * 20(natural number) = 80(natural number)
Subtraction– The closure property, which is applicable in multiplication and addition, is not applicable in the case of subtraction. The same goes for the commutative property.
Division– The commutative property, as well as closure property, does not apply to division as well.
Natural Numbers on a number line
The number line is a method of showing the position of different numbers. On the left-hand side of the number line, there are negative integers, and on the right-hand side, there are positive integers. In the middle of both sides lies the number 0. The position of natural numbers on the number line is the right side starting from 1 and extending to infinity.
Conclusion
Natural numbers are the kind of numbers that are not primitive and are most commonly used. All the other numbers have been discovered later on, and this one kind is what numbers were for people since the time the term numbers existed.
