October 26, 2020

Integers are widely used in many mathematical solutions. It deserves separate respect because it is one of the foundations of mathematics. When it comes to representation, integers have a unique way. If you are dealing with two integers and if someone asks you to represent them then we represent them in a graphical way. We call it **Comparing Integers**. So, what is comparing integers? Let's talk about that.

## Ordering Integers

Comparing integers is also known as ordering integer because what you will be doing is ordering the integers. In simple words, comparing integers means that you are ordering integers. The question is, how to order integers? If two numbers are represented graphically, the larger integer is situated to the right, and the smaller integer is to the left. There are some principles for ordering integers. With the help of these principles, you can order any integer you want.

## Criteria for Ordering Integers

### 1. Negative number vs Positive Numbers

Let's say you have two integers. One is a positive integer and another is the negative integer. We all know that the negative integer is always less than the positive integer. It doesn't matter that the negative integer has a high magnitude than the positive integer, it will always be less than the positive integer. The reason is simple, negative integers are less than zero. Now how will you show it? You will use a sign named **"Lesser Than" (****)**. Below is its representation:

You might be wondering what if is written on the right side? Then you need to reverse the sign. Since we know about the lesser than sign, now it's time for you to learn about the **"greater than"(****)** sign. Always remember, if you are changing the order, you need to change the sign as well otherwise it will have a different meaning.

### 2. Positive Integer vs Positive Integer

If you encounter two positive integers and asked to order them then it is easy. Order them like you always did. The higher the absolute, the bigger the number. Since you have knowledge about greater than and lesser than sign, why don't you try yourself first? You have two integers, one is and another is . Try ordering it yourself and we also did that so that you can tally your answer.

or

If your answer matches any one of the above that means you did it correctly.

### 3. Negative Integer vs Negative Integer

When you are comparing negative integers, there is a twist. As the magnitude of negative integer increases, its value decreases. In simple words, a negative integer is larger if it has a lower absolute value.

If you are wondering why we do this? It is because is closer to zero than and in negative integers, the more they are closer to zero the bigger they are.