Natural Numbers

Do you know the natural numbers ? In this article you will get to know them, understand their importance, how they are organized and what types of sets of natural numbers exist. Check it out and more!

Numerical language is present in our daily lives. Daily we read not only letters, but also numbers. Throughout school and professional life we ​​learn constantly, and mathematical literacy will be present.

In relation to numbers, today the standard adopted is the Indo-Arabic numeration system, which had its symbology conceived in antiquity by the inhabitants of the Indus River Valley, being improved over time and later spread by the Arabs.

This system of numbering is done by means of groupings of 10, because it is a Decimal Numbering System and has as base for the writing of any number the following figures:

1, 2, 3, 4, 5, 6, 7, 8, 9, 0

Set of natural numbers

In relation to numbers, the first numerical set is that of the natural numbers represented by the letter N. Mathematically this set is defined as:

Numbers that are integers and not negatives.

With regard to this definition:

• Whole is any element that is complete
• Not negative is any number greater than or equal to zero.

To better understand the definition of natural numbers follow the example below.

Example 1:

In this image it is possible to see that all the apples are integers, being then complete elements, we can use to count the natural numbers. In the image we have represented the drawing of 4 apples.

Already in this other image we can see that not all apples are whole, that is, they are not complete, so it is not possible to use the set of natural numbers in the count. It is important to understand that the set of natural numbers is used to count, and the zero may or may not be included in that count. This will be explained later in the text.

Types of sets of natural numbers

• Set of natural numbers including zero

N = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...}

• Set of non-zero natural numbers

N * = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ...}

Note : The three points at the end of the numerical sequence in the above sets represent an infinite sequence, ie it is possible to place more numbers within that set.

Also on the sets of natural numbers we have the following sets:

• Set of even natural numbers

N _pairs = {0, 2, 4, 6, 8 ...} = _odd N - N

• Set of odd natural numbers

N _odd = {1, 3, 5, 7, 9 ...} = N - N _pairs

• Set of natural prime numbers

N _primes = {2, 3, 4, 7, 11 ...}

Order of natural numbers

Natural numbers can be ordered in two ways:

• Ascending : Being ordered from the smallest to the largest.
• Descending: Being sorted from highest to lowest number.

Follow the example below.

Example 2:

Order the finite set of natural numbers below in ascending and descending order: {1, 5, 6, 3, 2, 4}.

Answer :
Ascending: {1, 2, 3, 4, 5, 6}
Descending: {6, 5, 4, 3, 2, 1}

Comparison of natural numbers

To compare the natural numbers we must use the symbols> (greater than) <(less than). Follow the examples below:

Example 3:

• 53 <70 (The natural number 53 is less than the natural number 70).
• 1220> 1219 (Natural number 1220 is greater than wild number 1219).

We can also use the symbols> and <to represent the ascending or descending order of a set of finite natural numbers, note:

Ascending:  1 <2 <3 <4 <5 <6 
Descending:  6> 5> 4> 3> 2> 1

I hope you have learned a lot from reading this text. Good studies!