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Ascending Order Mean in Math | Difference Between Ascending And Descending Order

September 8, 2022
written by Azhar Ejaz

Ascending order is when numbers or other items are listed from smallest to largest. An example of this would be if we were to put numbers on a number line from left to right – this would be in ascending order.

We typically denote ascending order by placing commas between the numbers or using the less-than symbol (<) between the numbers. For example, 1, 2, 3, 4, 5 or 1 < 2 < 3 < 4 < 5. The inverse method of increasing order is descending order, where the numbers are arranged in decreasing order of values.

In this article, you will learn the definition of ascending order, symbol/sign, examples, representation on a number line, and ascending order.

What Does Ascending Order Mean?

In mathematics, ascending order refers to the process of arranging numbers from smallest to largest from left to right.

It can also mean arranging letters or words in alphabetical order from A to Z.

Ascending means “going up”, so ascending order means that the numbers are going up. It is a way of ordering numbers. For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on. The less than symbol (<), is used to denote the increasing order. 

Ascending Order Symbol

There are two ways to represent a given set of numbers in ascending order: with commas ‘,’ or by using the less than symbol (<). The most common way to arrange numbers in ascending order is by using the less than symbol in between, which signifies that the number on the left is smaller in value than the number on the right side of the symbol. For example, 2 < 3 < 4 are all arranged in ascending order. For example,

1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9

The above numbers are arranged in ascending order from 1 to 9.

Difference between Ascending and descending order

Ascending OrderDescending Order
Numbers are arranged in increasing orderNumbers are arranged in decreasing order
Smallest to largestLargest to smallest
It is represented by less than a symbol: ‘<’It is represented by a greater symbol: ‘>’
Example: 3<6<7<9<10Example: 10>9>7>6>3

Example of Ascending Order

Some of the examples of numbers arranged in ascending order are given below:

  • 1 <  2 < 3
  • 10 < 11 < 12 < 13
  • 43 < 55 < 78 < 98 < 101
  • 100 < 1000 < 10000
  • -10 < -9 < -8 < -7

Ascending Order represent on Number Line

The concept of ascending order is introduced in primary classes for students of Class 1. With the help of the number line, students can understand the arrangement of numbers in increasing order.

The number line above shows numbers from -6 to 6 in ascending order. This means that the numbers on the left side of 0 are smaller than the numbers on the right side of 0. The further we go from left to right on the number line, the greater the value of the numbers becomes.

Frequently Asked Question-FAQs

What is ascending order?

Ascending order is simply a method of organizing numbers from smallest to largest value. The order goes from left to right and is sometimes referred to as increasing order.

What is a sign of ascending order?

Ascending order is represented by < (less than) symbol. For example, 3<5<7<9<11<13

What is descending Order?

When the numbers are written in decreasing order, i.e. largest to smallest value, then it is said to be descending order. For example, 13>11>9>7>5>3