Table of Contents

## INTRODUCTION:

We come across this term while doing maths. Mathematics is an integral part of our education system. Mathematics helps us to find ease in every prospect of our life. Starting from buying a product in the market to programming, maths is always the base of all. Here we can find the logic using basic and simple maths and then with that we can implement it using different languages. So today let us find out the different ways in which we can actually find out the logic behind performing a task using natural numbers in the field of programming.

## NATURAL NUMBER IN ENGLISH:

Well as we can see from the name, Natural numbers are those numbers that are already present in the number system and we use it to do basic calculations such addition, subtraction, multiplication or division. We get to know more about these numbers as we go deep down the maths and then slowly, we also use maths in order to perform the example works. Suppose when we want to give examples regarding any derivations or any other further examples, we can use these natural numbers in order to find the proper idea regarding the number. The same goes for the case of the computer where we get to execute different ways of finding the different programs or execute various types of performance.

## NATURAL NUMBERS:

Natural numbers are those numbers that start from1 and is extended till infinity.

Now, let us see how we can either print or implement the natural numbers using java:

For (i=1; i<=n;i++)

{

System.out.println(“the natural numbers are”,n);

}

This is the program snippet in java to print the natural numbers where n is the limit till where we would want to print the numbers.

## MATHEMATICAL UNDERSTANDING:

Mathematics is essential in a number of fields such as natural sciences, engineering, medicine, finances, and social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and some parts of game theory as well. The 1st step to Indian maths was kept by Aristotle who defined it as a science of quantity. Slowly with the increase in modernization and development, we are getting more and more focused on the technical parts that are also being a way to respond to artificial intelligence and many others.

## UTILITY IN PROGRAMMING LANGUAGE:

Any programming language be it java or python or c or c++, all of them basically uses the same snippet just with a different way of broadcasting them. just like the way the different television models have different attire to look at yet they all show the same shows at the same time.

Mathematicians have been using probability in a huge way in order to find than the maximum utility of maths in different fields and then from there now the computers have taken up a new way of understanding these theories mathematically so that it becomes easier for us to find the answer and code and decode it respectively.

There have been a number of terms such a data structure, DBMS and many others that have used the insight of mathematics but some of the simple logical applications still have the same amount of importance just as mathematics has in our lives.

## Algebraic Properties Satisfied by the Natural Numbers

The addition (+) and multiplication (×) operations on natural numbers as defined above have several algebraic properties: Closure under addition and multiplication: for all natural numbers a and b, both a + b and a × b are natural numbers. Associativity: for all natural numbers a, b, and c, a + (b + c) = (a + b) + c and a × (b × c) = (a × b) × c. Commutativity: for all natural numbers a and b, a + b = b + a and a × b = b × a. Existence of identity elements: for each number a, a + 0 = a and a × 1 = a. Distributivity of multiplication over addition for all natural numbers a, b, and c, a × (b + c) = (a × b) + (a × c). No nonzero zero divisors: if a and b are natural numbers such a × b = 0, then a = 0 or b = 0 (or both).

Read more – https://en.wikipedia.org/wiki/Natural_number

## CONCLUSION:

Thus, we have come to know that anything or everything can be implemented using the basic code of maths. The program snippets are all that require the computational knowledge which shall help us to make our work much easier and user-friendly in any of the programming languages that we want to use. Any further increase in the programming would equally need the help of mathematics in order to find out the solutions to various problems.

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