Predecessor and Successor

First of all, what do we mean by the word successor and predecessor? The term successor means ‘the one which comes immediately after. The term predecessor means ‘the one which comes before. Whatever might be the context, the one which comes after this is called a successor and the one which comes before is called a predecessor. As we are talking about mathematics here, we need to talk about these two terms with respect to numbers.

Definition of successor

This number is referred to as a successor because it comes immediately after the original. In other words, it is called the successor of a particular number if it comes immediately after it.

A whole number that has an additional digit is the successor of a whole number. 

How is the successor of a number calculated?

We can observe that each whole number has a numerical successor whose calculation is:

Given Number + 1 = Successor

Example of successor 

For example –

• 1,000 is the successor of 9,999

• The successor of 1,00,999 is (1,00,999 + 1) = 1,01,000

In mathematics, the successor is the number that results from adding 1 to a whole number.

Definition of the predecessor

Usually, predecessors are numbers that occur immediately before a particular number. In other words, predecessors are the numbers that come before a specific number.

A number less than the given one is the predecessor of whole numbers.

Method to calculate the predecessor of a number?

We can observe that every whole number has a numerical predecessor whose calculation is:

Given Number –  1 = Predecessor 

Example of the predecessor 

For example – 

• 999 is the predecessor of 1,,000

• The predecessor of 70,85,000 is (70,85,000 – 1) = 70,84,999

In mathematics, the predecessor of a specific number results from adding 1 to a whole number.

From the above understanding, we can conclude the successor and predecessor in a simple format that is easy to understand and remember.

With the help of examples, explain what successor and predecessor mean for a number.

PREDECESSOR          NUMBER          SUCCESSOR

   (100 – 1) 99                   100                 (100 + 1) 101

The predecessor and successor on number-line

As the name whole number itself says, it is whole, i.e., not a fraction or decimal, so fractions are not part of whole numbers. And because of this, it is not a fraction if it is a whole number, so it can not be negative. The counting numbers are also contemplated as the whole numbers. The concepts of the successors and the predecessors are applied only to whole numbers.

Going in a forward direction – The successor of a number is lying immediately next to the number after the specified number.

Example 6 is the successor of 5 since it lies immediately next to 5.

Going in a backward direction – The predecessor of a number is lying immediately before the number after the specified number.

Example 3 is the predecessor of 4 since it lies immediately before 4.

Difference between predecessor and successor

Let’s understand this topic step by step

Consider the following situation: Say we have a number ‘ X ‘than those who succeeded and those who preceded those number areas – 

( X + 1 ) and ( X − 1 )

Using the following comparison, we can tell the exact successors and predecessors differ from each other for a specific number:

( X + 1 ) – ( X − 1 ) = 2

Therefore, there is a difference of two between the preceding and the succeeding. Hence, the interpretation can be written as:

SUCCESSOR – PREDECESSOR  = 2

Important Note

There is an important point to be discussed, namely that successors and predecessors are applied only to whole numbers. It implies that these formulae can also apply to zeros, ones, twos, etc.

In addition, neither successor nor predecessor applies to fractions, decimals, and natural numbers. As a result, there is a whole number that is the successor of every whole number as well, as all the whole numbers except zero have a predecessor.

Conclusion

Thus in this article, we have learned the concepts of the successor and the predecessor and how to compute those who succeeded and those who preceded that particular number along with a few examples. We have also briefly seen that the successors and the predecessors differ from each other. These concepts are useful in the fields of mathematics and science.