Natural Numbers
The set of all natural numbers, normally is denoted by math symbol N.
Individual way of building the natural numbers is during an interactive 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.
The counting of objects in numbers 1, 2, 3 .... is known as natural numbers.
Then N = {1, 2, 3, 4 ....}
The set of positive integers +1, +2, +3, ..... are called natural numbers.
N = {+1, +2, +3 ....}
Clearly, the set N of natural number is an infinite set. The sum and product of two natural numbers are always a natural number. The natural numbers in the number line:
The order relations in Q can be exhibited pictorially by means of a straight line called the number line. For this, we draw a straight line, say l, which extends in both the directions endlessly as indicated by the arrowheads.
Can Natural Numbers be Negative
No, the natural numbers are all positive numbers that starts from 1 (Even they are called counting numbers).
List of Natural Numbers
Natural numbers are beginning with 1 and increasing one by one. The set of natural numbers is denoted by the symbol N. In the set of natural numbers, 2 is called the successor of 1. 1 is called the predecessor of 2 and 3 is called successor of 2 and 2 is called predecessor of 3. After the element 3 to indicate that the other elements of N are listed following the pattern of 1, 2, 3.
The set of odd, even and prime numbers except zero is called as natural number. The result of addition and multiplication of numbers always gives natural number. The notation used for natural number to represent it mathematically is N.
Let N be the set of natural number as N = {1, 2, 3,…..}
The set of natural numbers may be finite or infinite. The finite defines the numbers in the set are countable. Infinite set means the numbers are uncountable. The natural numbers are well-ordered contains only positive integers.
No, zero is not a natural numbers. The natural numbers are always greater than zero. This natural numbers are used to count the things(thy are called counting numbers) so they wont consider zero a natural number.
Counting produced the numbers one, two, three, etc, which now are called set of natural numbers. The collection of all natural numbers are represented by the English letter N. Even though it is not possible to list all the elements of N, we write N = {1, 2, 3 …}.
Natural numbers are involved in the following algebraic properties-
Property | Addition | Multiplication |
Closure | a + b | a × b |
Associative | a + (b + c) = (a + b) + c | a × (b × c) = (a × b) × c |
Commutative | a + b = b + a | a × b = b × a |
Identity | a + 0 = a | a × 1 = a |
Distributive | a × (b + c) = (a × b) + (a × c) | |
Zero divisor | a × b = 0 then a = 0 or b = 0 | |
Here are the natural numbers examples:
Solved Examples
Solution:
a + b = 5 + 6 = 11
b + a = 6 + 5 = 11
So, a + b = b + a for a = 5, b =6.
So, closure property of addition holds for the numbers 5 and 6.
Solution:
Putting the values a = 5 and b = 6.
a x b = 5 x 6 = 30
So, closure property of multiplication holds for 5 and 6.
Solution:
a + (b + c) = (a + b) + c
5 + (4 + 3) = (5 + 4) + 3
5 + 7 = 9 + 3 12 = 12
So, associative property of addition holds true for 5, 4 and 3.
Solution:
a x (b x c) = (a x b) x c
5 x (4 x 3) = (5 x 4) x 3
5 x 12 = 20 x 3
60 = 60
Solution:
a + b = b + a
5 + 4 = 4 + 5
9 = 9
So, commutative property for addition holds for 5 and 4.
Solution:
a × b = a × b
5 x 4 = 4 x 5
20 = 20
So, commutative property for multiplication holds for 5 and 4.
Solution:
a + 0 = a
5 + 0 = 5
So, identity property for addition that holds for 5.
Solution:
a × 1 = a
5 x 1 = 5
So, identity property for multiplication that holds for 5.
