Have you heard of the Natural Numbers? They are used all the time in our daily lives and, many times, we don't even notice. Want to see it? Think about answers to the following questions: How old are you? What's your phone number? How many titles has Brazil won at the World Cup? For all these questions, we need the numbers natural to express the answer!
Natural numbers are used in counting, to establish an order, a code or to make a measure. The sequence formed by the natural numbers and used in all situations is: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... We can use the symbol 
to represent this numerical set:
= {0, 1, 2, 3, 4, 5, 6, 7, 8...}
Note that the set of natural numbers starts with the number zero, but it doesn't have a final number, that's why we say that the natural ones are infinite! From this set, we can establish several others infinite sets, let's see some:
Set of natural numbers without zero: * = {1, 2, 3, 4, 5, 6...}
Set of even natural numbers = {0, 2, 4, 6, 8, 10...}
Set of odd natural numbers = {1, 3, 5, 7, 9, 11...}
set of prime natural numbers = {2, 3, 5, 7, 11, 13...}
By establishing a relationship between two or more numbers, we end up ordering them. The numbers that make up the set of natural numbers are ordered, and some terms can be used to describe this order:
Predecessor:
We say that the predecessor of a number is the one immediately preceding it. For example, the number 3 is predecessor of 4; 2 is predecessor of 3; 1 is predecessor of 2; 0 is predecessor of 1 it's the 0 it does not have a natural predecessor.
Successor:
If the predecessor is the one that comes before, the successor of a number is the one that comes immediately after. We have to 1 is successor of 0; 2 is successor of 1; 3 is successor of 2; 4 is successor of 3 and so on.
Consecutive:
We say that certain numbers are consecutive if no number is missing between them. For example: 1, 2 and 3 are consecutive, 4 and 5 are consecutive and 11, 12, 13, 14, 15, 16 and 17 are consecutive.
We can even make comparisons between natural numbers. For this, we will use the following symbols:
= (equal)
> (greater than)
Let's look at some comparisons between some natural numbers:
2 = 2 (two equals two)
5(five less than seven)
1 > 0 (one greater than zero)
3(three less than eight)
10 > 5 (ten greater than five)
11 (eleven under seventeen)
12 > 1 (twelve greater than one)
By Amanda Gonçalves
Graduated in Mathematics
Take the opportunity to check out our video lesson on the subject:
