Natural numbers

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What are natural numbers?

Natural numbers are those that allow counting or ordering the elements of a set. There is no total or final amount of natural numbers, therefore, natural numbers are infinite. It is considered a natural number from number 1.

Natural numbers belong to the set of positive integers, therefore they have no decimal part, are not fractional, or imaginary part and are to the right of zero on the line.

Natural numbers can be represented in a straight line and are always ordered from least to greatest.

• 1
• 2
• 3

Learn more about: “Signs of greater or lesser”. →

The number zero "0" is sometimes considered a natural number, but generally it is not.

• The Set theory include zero within the group of natural numbers.
• The Number theory he prefers to exclude zero from the group of natural numbers.

Curious fact: Natural numbers were the first set of numbers used by humans to count objects.

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Which are the natural numbers?

The natural numbers are unlimited, if we add 1 to a natural number, we get another natural number, these are represented by the letter "N", in uppercase. The natural numbers are: N = {1, 2, 3, 4, 5, 6,…, 10, 11, 12,…, infinite}

Properties or characteristics of natural numbers

• They have an initial element, depending on the author can be "0" or "1".
• Every natural number has a unique successor, that is, each natural number has a consecutive natural number.
• Two different natural numbers cannot have the same successor.
• The set of natural numbers is infinite.
• Between two consecutive natural numbers there is no other natural number, for that reason it is considered as a discrete set.

Operations with natural numbers

When performing a sum or multiplication operation using natural numbers, another natural number will always result.

When performing a subtraction or division operation using natural numbers, the result will not always be another natural number. The following examples show possibilities in which a natural number is not found:

5 - 9 = -4
-7 +4 = -3

The result of the subtraction is a negative number, for that reason it is not considered a natural number.

1/2 = 0.5
1/3 = 0.3333...

The result of the division is not an integer since it has decimals, for that reason it is not considered a natural number.

Whole numbers are those that contain negative numbers and natural numbers.