A number is an integer value used to express the quantity of an item and to aid calculations. The numbers are divided into two categories: real and imaginary. In this post, we’ll go through the sub-categories of real numbers known as even and __odd numbers__ in depth. We’ll look at the description, examples, and properties of even and odd numeric values.

Contents

## Explanation of Even and Odd Numbers:

The stated example for even and odd numbers are given as follows:

Statement 1: Explains that even numbers are those numbers in the number system that are divisible by the number 2 and odd numbers are numerical values that are not divisible by two.

Statement 2: Explains that even numbers are those numerical values that when divided by number 2 leaves no remainder or answer left while odd numbers are those numbers which when divided by number 2 leaves a remainder of number 1 or more.

### Set Representation of Even and Odd Numbers

An even equation is written as an integer of the form n = 2k, where k is an integer. An integer of the form n = 2k + 1 is known as an odd number. Only integers are classified in this way. 1/2, 4.201, and infinity are non-integer numbers that are neither even nor odd. The sets of even and odd numbers can be denoted as:

- Even = {2k : k ϵ Z}
- Odd = {2k + 1 : k ϵ Z}

## Characteristics of Even and Odd Numbers:

- The sum of two even numbers in a number set is an even number
- The sum of two odd numbers in a number set is invariably an even number
- The sum of even and an odd number is a number set is an odd number
- Even number is divisible by 2 and leaves the remainder 0 which means there is no answer left
- An odd number is not completely divisible by 2 and leaves the remainder 1 or more than one.
- An even number invariably ends with 0, 2, 4, 6, and 8
- An odd number invariably ends with 1, 3, 5, 7, and 9

## How to Check if it is an Even or Odd Number?

We know that __even numbers__ that end with 0,2,4,6,8 numeric values and odd numbers are those numbers that end with 1,3,5,7,9 unit digits.

So, the first step is to view the number in the ones or the units place. This single digit will tell you whether the entire numerical is odd or even in nature.

Let us take the number 132 as an example. To check whether the respective number is even or odd, first, divide the number by number 2.

When dividing the number 132 by 2, we see that it is divisible by number 2 and thus matches the criteria. So, the given number 132 is an even number.

## What are Even and Odd Decimals?

Since decimals are not whole numbers, they are neither even nor odd. You can’t assume that the fraction 1/3 is odd because the denominator is an odd number, or that the fraction 12.34 is even because the last digit is even. Decimals and fractions cannot be even or odd since only integers can be even or odd. Zero, on the other hand, is an integer and is divisible by two, making it an even number.

## Fun Facts

- Every alternate number in the counting in the number system is an even number starting from 2 and an odd number starting from 1.
- Zero, the starting of positive numbers is an even number.
- The great ancient Greeks made use of shapes and figures with an odd number of sides to represent the odd numbers in the number system.
- The Pythagoreans used the terminology “gnomon” for expressing the odd numbers