While dealing with a set of numbers many a times a need arises to arrange the numbers in a certain order. The numbers can be arranged from the least valued number to the highest number or vice versa. When the least valued number comes first and the highest valued number comes last then it is known as ascending order. In an arrangement, when the highest valued number comes first and least valued number comes last then it is known as descending order. The set can have repetition of numbers also. If there are repeating numbers in the set then ascending order arrangement becomes non decreasing order and descending order arrangement becomes non increasing order.

The kind of arrangement of a set of numbers in which the lower value will always come before the higher value is known as ascending order. It is the non decreasing order of arrangement which can also be said increasing order if there is no repetition of numbers. This process of ordering a number is also known as sorting. There are various algorithms present for sorting a set of numbers. Bubble sort, quick sort, selection sort are to name a few of those algorithms.For example, we have two numbers 7 and 9. We can easily compare and order them as 7, 9 in ascending order.

If we have a set of numbers 6, 4, 9, 11, 1, 13, 5 then the ascending order will be written as:
1, 4, 5, 6, 9, 11, 13

Suppose we have repeating numbers in the set. We are being given the set as 6, 4, 6, 7, 13, 8, 11, 8. The dorting will be done as given here:
4, 6, 6, 7, 8, 8, 11, 13

This is called the non decreasing order as it is not necessary that the value of number is increasing as they can remain constant also but the values are not decreasing as we go ahead.
The given steps should be followed to write a given set of numbers in ascending order.

1) Find the smallest number of the set and write at first place.

2) Exclude that number from the set.

3) Find the smallest number of the new set and write it at the next place.

4) Repeat steps 2 and 3 till the set becomes empty.

For example, we have been given a set 5, 7, 9, 2, 1. Let the set be S. Finding the smallest number we get 1. Hence, we write the sorted set as, S1 = 1.

Excluding 1 from the given set we have the set S = 5, 7, 9, 2. The smallest number here is 2. We will write it at the next place in the sorted set.
S1 = 1, 2

Excluding 2 from the set S we get, S = 5, 7, 9. The smallest value is 5. The sorted set becomes S1 = 1, 2, 5.

Excluding 5, the set S = 7, 9. The smallest value is 7. The sorted set becomes S1 = 1, 2, 5, 7.

Excluding 7, set S = 9. The only value is the smallest value. Putting 9 in the sorted set it becomes,
S1 = 1, 2, 5, 7, 9.

Now, excluding 9 the set S becomes empty. Hence, the given set in ascending order can be written as S1. That is,
1, 2, 5, 7, 9
Example 1: Write the given set of numbers in ascending order.
123, 101, 657, 326, 178, 216

Solution: 
The smallest number is 101.

Second smallest 123. Next number 178. Then, 216. The next number is 326. The last number left is 657.

Hence, the ascending order is 101, 123, 178, 216, 326, 657.
Example 2: Find the mid value of the given set of numbers.
54, 19, 23, 14, 68.

Solution:
As we have been given 5 values we need to find the third value if the numbers are sorted in ascending order. Let us first write the numbers in ascending order. Let us see step by step.

1) Find the smallest element.
14

2)
Excluding 14, find the smallest element and write at the next place.
14, 19

3) Excluding 19 again and find the next smallest we get the sorted set as,
14, 19, 23

4) Excluding 23, the next smallest number is 54. Writing it at next place we have,
14, 19, 23, 54

5) The last number is 68. Hence, the sorted set becomes,
14, 19, 23, 54, 68

The number at the third position is 23. Hence, the mid value of the given set is 23.