Natural Numbers: Definition, Representation and Arrangement

Do you want to know how natural numbers are represented? What are natural numbers? Next I’m going to explain the definition of natural numbers, how they are represented on the number line, how they are ordered and how they compare to each other.

What are Natural Numbers

Natural numbers are the set of numbers that allow us to count and order things. They are the first numbers we are taught at school, when we learn to count:

how natural numbers are represented

  • Through cardinal numbers we can count:
    • There are 4 trees in the park.
    • I have 3 coins.
  • Through the ordinal numbers we can order:
    • Next year I’ll be in the second year.
    • I finished fifth in the race.

The natural numbers therefore are those that go from 1 forward: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11… in other words, they are positive numbers.

The set of natural numbers is represented by the letter Ν:

Ν={1, 2, 3 , 4, 5, 6, 7, 8, 9, 10, 11 ,12…}

How Natural Numbers are Represented

To represent the natural numbers on the number line we do it following the following steps:

1. Draw the line, divided into equal parts and place the 0 on the left:

Representation of natural numbers

We place numbers to the right of zero, increasing their value one by one, from left to right:

con que letra se representan los numeros naturales

And so we could go on to infinity 🙂

How Natural Numbers are Ordered

Let’s learn how these numbers are ordered and how they compare to each other.

Ordination of Natural Numbers

The natural numbers represented on the line are placed from left to right, increasing their value one by one, that is, they become larger. Therefore, they are placed from lowest to highest, from left to right.

The sense of ordering and representation is the same:

representation of natural numbers

The more to the left the number is represented on the line, the smaller it will be. The smallest natural number is 1. The largest, as we have said before, does not exist because natural numbers are infinite.

Comparison of Natural Numbers

To compare two numbers with each other we use the following symbols:

  • > (is greater than)
    • 5 > 2 (5 is greater than 2)
  • < (is less than)
    • 4 < 9 (4 is less than 9)

To learn the meaning of these symbols you can use the rule that “the big one always clicks on the little one”.

The third symbol is better known:

  • = (is the same as)
    • 3 = 3 (3 is the same as 3)