In the world of mathematics there are many types of numbers and many different ways to classify them. Therefore, if we want to be mathematical experts, it is vitally important to know how to express each one in the best possible way. One of the most common are the natural numbers, which are the ones we usually use on a regular basis in our day to day. However, there are also irrational numbers, which in more advanced levels of mathematics are also often used since they express another mathematical state that is applied in many operations.
For this reason, and more especially if you are going to develop a career in mathematics, it is important, in addition to mastering operations as basic as adding, to know how to differentiate the different types of numbers, especially natural ones.
What are the natural numbers?
If we think of natural numbers, the first thing that comes to mind is the set of numbers that can be counted. Therefore, the first characteristic of this type of number is that they are rational and integers. In mathematical language we can talk about exact or inexact numbers. The wild type are exact. In this sense, they allow us to carry out the review of a set of inputs. For example, if we open the fridge we can count what we have thanks to natural numbers. If we have three pears and two apples, these two records are natural numbers.
On the other hand, the net salary can be in natural numbers or be in decimals and, therefore, it would no longer be a natural numbering. Throughout history, the natural numbers are the ones that appear first. Basically because there was a need for humans to count the objects they had. In fact, before coins such as drachmas in Greece or sesterces in Ancient Rome began to be minted, commercial activity was based on the exchange of goods. For example, I give you meat and you give me fish. Therefore, in this type of act, the natural numbers played a really important role.
In the history of the natural numbers there is also room for controversy. In fact, in many mathematical theories the same thing happens. We are talking about zero, which some include within the set of natural numbers such as Set theory, considering that it serves to express a totally null set without objects. On the other hand, others like those of Number Theory prefer to leave it out. They think that the fact of giving meaning to the null does not fall within the definition of this type of numbers. Thus, this continues to be one of the great debates in the mathematical world.
At a general level we could define that this type of numerical set has two main objectives. On the one hand, there is the cardinal, that is, giving quantity to a set. If we have two pears we have two pears and if we have three apples we have three apples. In addition, it also has an ordinal value. In this sense, if we have three pears we will always have more than two apples. For this reason, the finite set of natural numbers deciphers the quantity but also the order of each of these types of quantities. In a more colloquial context, it also serves to differentiate all the elements of a set. On a practical level we could say the members of a football club. Each of them has a card that differentiates them from the rest and gives them a specific seat. In this way, partner 90.158 is different from 20.743. It is another of the fields of natural numbers.
Benefits of knowing the natural numbers
All in all, knowing the natural numbers allows us to benefit from different aspects throughout our personal and professional lives. The most prominent are the following:
- Know how to count From a very young age, one of our great objectives is to know how to count. In addition to speaking, since it allows us to communicate with other people, counting is essential to start our development as people.
- Know the numbers. To speak you must know the words, while to count you must know the numbers. The natural types are one of the first groups that we will begin to learn in school when we begin our education.
- Perform mathematical operations. Some really simple calculations such as addition, subtraction, multiplication or division use natural numbers in most cases. Therefore, it is necessary to know them in depth.
- Learn to start classifying numbers. If you want to carry out higher studies, it will be necessary to know how the different numbers that we can find are classified. Therefore, you should start with the natural numbers, the simplest in most cases.
Therefore, if you know the natural numbers you can begin to deepen your mathematical knowledge both at the user and professional level.
How to classify natural numbers?
The natural numbers are those that, moreover, can be found on the calculator. This device, not to be confused with the love calculator, allows us to perform mathematical operations of different kinds depending on the type of intelligence that the device has. For this reason, we can find different types that only allow addition, subtraction, multiplication and division to others that can calculate different types of logarithms, including naperians.
Also, the natural numbers can be represented in a straight line ordered from greatest to least. In this way, eight will always be greater than three. However, another of the great current debates involves whether the natural numbers are infinite or not. Some argue that they have an ending, while others do not since adding one more unit is enough to create a new number.
When classifying this type of number, you should know that those of the natural type belong to those of the positive integer type. In this way, those that have a decimal part such as 1.5 are excluded, among them, in addition to fractions. 0.5, that is, a half part, could also be expressed as 1/2 since if we divide one by two, the result is 0.5. Furthermore, all natural numbers lie to the right of zero on the representation line. Thus, all numbers that are negative and that are therefore represented to the left of zero itself are also excluded.
The natural numbers, one of the most used
When establishing mathematical operations, the natural numbers are the main one that is learned. If we operate with this type of numbers, the results will always be closed and in the form of a natural number, except in subtractions. For example, if we add we will always have a positive and natural number. The same goes for multiplication and division. On the other hand, with subtraction we have the possibility that we have a natural number or not. It will depend if the result is a negative number or not. For example, 12-7 will give 5, a positive and natural number. However, 7-12 will result in -5 and, therefore, we will be dealing with a negative number that is not natural.
They are one of the most used throughout history. In this sense, the first samples of natural numbers are found in ancient Mesopotamia thousands of years ago. Clay tablets were used to start writing numbers. Later, in ancient Greece, writing and numbering continued to be developed. However, the Romans were the ones who made great advances in terms of natural numbers using a numeral system that is currently studied in schools. Latin was the precursor to much of today’s European language. Thus, signs like I, V, X, L or C can be translated by numbers like one, five, ten, fifty or one hundred. The combination of these letters allowed to combine the different natural numbers that we can find today.
Finally, we want to recommend some of the main characteristics of the natural numbers as a summary. In all cases, and always leaving aside the debate about whether he considers zero to be a natural number, a natural number succeeds another natural number. When we operate with natural numbers we will always find a finite number of natural numbers. Furthermore, every natural number will always have a natural number greater than this. This last characteristic would serve to reinforce that the natural numbers are infinite in character. If these had an end, obviously this definition could not be applied because the number that marked the end of the numbering would be the greatest of all, and would not have another number that could be greater than it.
For this reason, natural numbers are of vital importance for all those who want to perform mathematical operations. Don’t forget that not knowing this type of numbers can end up being a burden to know another type of numeration such as irrational numbers because in the end they all share some characteristics with the natural numbers. In this way, these are the first to be learned in any of the cases that one wants to delve into them.