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Natural Numbers

The set of all natural numbers, normally denoted by math symbol N. Individual way of building the natural numbers is during an iterative process starting from the empty set.

Natural numbers happen naturally (hence the name) from counting objects. Because of this fact, the fundamental operations of arithmetic are addition, subtraction, multiplication and division can be explained in naturally appealing ways for natural numbers before being extended to larger sets of numbers.

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Natural Numbers Definition

The counting of objects in numbers 1, 2, 3, … are called natural numbers.

Then N = {1, 2, 3, 4, …}

The set of positive integers +1, +2, +3, … are called natural numbers.

N = {+1, +2, +3, …}

The set of natural number is an infinite set. The sum and product of two natural number are always a natural number. The natural numbers on the number line: Properties for Natural Numbers

Below are properties of natural numbers-

 Property Addition Multiplication Associative p + (q + r) = (p + q) + r p * (q * r) = (p * q) * r Commutative p+ q = q + p p * q = q  * p Identity p + 0 = p p * 1 = p Distributive p * (q + r)  =  (p * q) + (p * r) Zero divisor p * q = 0 then p = 0 or q = 0

Examples

Here are the natural numbers examples:

Example 1 :

If p = 4, q = 1 and r = 3.  Use associative property for addition and  Multiplication.

Solution:

Associative property for addition is p + (q + r) = (p + q) + r

4 + (1 + 3) = (4 + 1) + 3

4 + 4 = 5 + 3

8 = 8

Associative property for multiplication is p * (q * r) = (p * q) * r

4 * (1 * 3) = (4 * 1) * 3

4 * 3 = 4 * 3

12 = 12

Example 2:

If p = 10 and q = 11.  Use commutative property for addition and for multiplication.

Solution:

Commutative property for addition is p + q = q + p

10 + 11  = 11 + 10

21 = 21

Commutative property for multiplication is p * q = q * p

10 * 11 = 11 * 10

110 = 110

 More topics in  Natural Numbers Properties of Natural Numbers Natural Numbers Examples
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