Maths is a subject of logic. We learn here a huge number of concepts and the interlinking between them. The basics of mathematics begin with numbers. In our primary classes, we have learned different types of numbers such as whole numbers, natural numbers, even and odd numbers, etc. In real life, we have many applications of these numbers. For example, we use natural numbers for counting purposes, such as 1,2,3,4,5,6,7,8,…and so on. Therefore, they are also called counting numbers.
An interesting fact about these natural numbers is that each successive number is greater than the preceding number, i.e. 2 is greater than 1, 3 is greater than 2, 4 is greater than 3, and so on. Such an arrangement of numbers where the numbers are represented in increasing order is called ascending order. The symbol used to arrange the numbers in ascending order is ‘<’, also called less than a symbol. Therefore, we can arrange the natural numbers using the symbol here, such as:
1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10…<(infinity)
In the similar manner, the whole numbers are also arranged in ascending order, as they consist of all positive integers and zero.
0 < 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10…<(infinity)
When we talk about integers, it consists of all the positive and negative integers including zero. Also, in the number line, the integers are arranged in ascending order, such as:
…-10 < -9 < -8 < -7< -6< -5< -4 < -3< -2< -1< 0< 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10…
So for any group of numbers, if we need to arrange them in increasing order, then we have to put the smaller numbers first followed by less than symbols and then put the number which is only greater than the first number and so on.
Now, similarly, we can arrange the numbers in decreasing order of their values. In this case, we take the larger number from a group of integers, first, and then arrange the rest of the numbers in decreasing order. This type of arrangement is also called a descending order.
When in a series, if each successive number is smaller than each preceding number, then the arrangement of numbers in the series is known as descending order. The symbol used to show the arrangement of decreasing numbers is ‘>’, which is also called greater than symbol. Let us arrange the first 10 natural numbers in descending order.
10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1
The above arrangement signifies, 10 is greater than 9, is greater than 8, is greater than 7, and so on. Hence, 10 is the largest number here.
Similarly, we can arrange the whole numbers as well, such as:
10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > 0
Hence, here 0 is the smallest value.
If we arrange all the integers including 0 in descending order, we get:
…10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > 0 > -1 > -2 > -3 > -4 > -5 > -6 > -7 > -8 > -9 > -10…
Therefore, we here conclude that:
Ascending Order → Smaller Value to Largest value
Descending Order → Largest Value to Smaller Value
These were the basics of arranging the numbers in Maths. The major applications of both ascending and descending orders can be seen while solving the problems related to series and sequences.
