Even and odd numbers

Even and odd numbers

Let's enter in the world of numbers. There are several categories of numbers like integers(positive integers and negative integers), rational numbers, irrational numbers, whole numbers, fractions and much more. The integers (both positive and negative) can also be categorised as Even numbers and odd numbers. 

   So, Let's start with even and odd.

  Definition of Even and odd numbers:

An integer number (positive or negative) which is   divisible by two(2) is called an even number.

On, the other hand, an integer number (positive or negative) which is not divisible by 2 is called a odd numbers.

 So, it is very clear that, an even number is not a odd number and a odd number is not an even number.

  As for example,  8 is  divisible by 2 .So it  is an even number. But,  9  is not divisible by 2 . So, it is odd  a number.

The even and odd numbers can be defined in an another interesting way.

  An integer is called an even number if it has no remainder(or, remainder is 0) when it is divided by 2 . Similarly, an integer is called a odd number if it has remainder '1' when  it is divided by 2.

 As for example, 6 has no remainder when it is divided by 2. So, it is an even number.

But, 5 has remainder '1' when it is divided by 2. So, 5 is a odd number.

In  a  more formal way we can define even and odd numbers.

 A number  m  is called an even number if it can be expressed as , m= 2n such that n is an integer.

 Again, a number  k is called a odd number if it can be expressed as , k=2n+1 such that n is an integer.

 Here, 4 can be expressed as, 2×2 +0. So, it is an even number. And, 7 can be expressed as, 2×3 +1 . So, it is a odd number.

Basic operations with even and odd numbers:

(1) even number+even number=even number.

Example: 12+6=18.

(2) even number+ odd number =odd number.

Example:  24+5=29.

(3) odd number+odd number=even number.

Example:  5+7=12.

(4) even number - even number= even number.

Example: 8-4 =4.

(5) even number - odd number= odd number.

Example: 10-5=5.

(6) odd number - odd number = even number.

Example, 7-5=2.

(7) even number × even number= even number.

Example: 8×4=32.

(8) even number × odd number = even number.

Example: 4×7=28.

(9) odd number× odd number= odd number.

Example: 5×3=15.

Zero is an even number.

Yes , it's true. Zero is an even number.

Here is the proof.

 Zero is divisible by 2. Also, 0 can be expressed as, 0= 2×0.

So, it is clear that, 0 is an even number.

Here are some even and odd numbers.

 Even numbers: 0,2,4,6,8,10,12,14,16,18,20,...

 Odd numbers: 1,3,5,7,9,11,13,15,17,19,...

   

 If you find out any incorrect information or know anything more about this , please write it in the comment section!