Successor and Predecessor

Successor and Predecessor

Nov 30, 2022, 16:45 IST

Successor and Predecessor are the two terms in Mathematics that are most commonly used for the sequence and series of whole numbers. The Successor is defined as after numbers (that appear just after), and the Predecessor is known as before numbers (that occur just before).

What are the Successor and Predecessor?

The term Successor and Predecessor in mathematics means following directly after or before a particular number. Both successors and predecessors essentially only applied to whole numbers. The successor is referred to as after the numbers, while the predecessor is referred to as before the numbers.

Successor in mathematics refers to the following term of a particular term, while predecessor in mathematics refers to those before a specific term. We can find the successor of a whole number by adding one to the given number, while to find the predecessor of a whole number, we subtract one from a specific number. In this short article, we will study what are successor and predecessor, the meaning of successor and meaning of predecessor, how to find the successor of a given number, how to find the predecessor of a given number, etc.

Successor Meaning

A Successor is a term that comes immediately after/right after a particular number or term, or value. Suppose n is a number (where n belongs to any whole number), then the successor of n is ‘n+1’. The other terminologies used for a successor are just after, immediately after, and next number/next value.

Examples of Successor

• If n = 5, then successor of 5 is 5 + 1 = 6
• If n = 10, then successor of 10 is 10 + 1 = 11
• If n = 20, then successor of 20 is 20 + 1 = 21
• If n = 50, then successor of 50 is 50 + 1 = 51
• If n = 100, then successor of 100 is 100 + 1 = 101

Predecessor Meaning

A Predecessor is a value that comes immediate before/right before just before a particular value. Assume a value x (where x belongs to any whole number), then the predecessor of x will be x-1. Thus, to find the predecessor of any value, we have to subtract the given value from 1.

Examples of Predecessor

• If x = 5, then predecessor of 5 is 5-1 = 4
• If x = 10, then predecessor of 10 is 10-1 = 9
• If x = 20, then predecessor of 20 is 20-1 = 19
• If x = 50, then predecessor of 50 is 50-1 = 49
• If x = 100, then predecessor of 100 is 100-1 = 99

Role of Whole Numbers

One thing to remember is that the successor and predecessor only apply to entire numbers. This means they use zero, one, two, three, and so forth.

They do not apply to negative numbers, fractions, or decimals. In addition, every whole number has to have a successor. Except zero, every whole number has a predecessor.

How to Find Successors and Predecessors?

To calculate both the successor and predecessor of any value, we have to apply the primary method of addition and subtraction. In the successor, we need to add 1 to the given number, whereas in the predecessor, we always need to subtract 1 from the given number. To find a successor and predecessor is very simple and quick.

• Successor = Given number + 1
• Predecessor = Given number – 1

Difference Between Successor and Predecessor

Solved Examples

Q1. Find the successor of the following numbers.

1. 12
2. -12
3. -84
4. 90
5. 150
6. 45
7. 89

Ans. The required successors are:

1. 12 → 12 + 1 = 13
2. -12 → -12 + 1 = -11
3. -84 → -84 + 1 = -83
4. 90 → 90 + 1 = 91
5. 150 → 150 + 1 = 151
6. 45 → 45 + 1 = 46
7. 89 → 89 + 1 = 90

Q2.  Write the predecessor and successor of

1. 20
2. 1997
3. 12000
4. 49
5. 100000

Ans.

A. 20

Predecessor of 20 → 20 – 1 = 19

Successor of 20 → 20 + 1 = 21

B. 1997

Predecessor of 1997 → 1997 – 1 = 1996

Successor of 1997 → 1997 + 1 = 1998

C. 12000

Predecessor of 12000 → 12000 – 1 = 11999

Successor of 12000 → 12000 + 1 = 12001

D. 49

Predecessor of 49 → 49 – 1 = 48

Successor of 49 → 49 + 1 = 50

E. 100000

Predecessor of 100000 → 100000 – 1 = 99999

Successor of 100000 → 100000 + 1 = 100001

Q3. What is the successor of the largest three-digit number?

Ans . The largest three-digit number is 999. Therefore, the successor of 999 is 1000.

Q4. What is the predecessor of the smallest three-digit number?

Ans. The smallest 3-digit number is 100. Therefore, the predecessor of 100 is 99.

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Frequently Asked Question (FAQs)

Q1. What is the successor in Maths?

Ans. In Mathematics, the successor of any number is the value that comes immediately after the given number. If x is a number, then its successor is x+1. For example, the successor of 66 is 67.

Q2. What is a predecessor in Maths?

Ans. In Mathematics, a predecessor of any number is the value that comes immediately before the given number. If n is a number, then its predecessor is n – 1. For example, the predecessor of 10 is 9.

Q3. What is the successor of 23?

Ans. The successor of 10 is 23 + 1 =24.

Q4. What is the predecessor of 4499?

Ans. The predecessor of 499 is 498.

499 – 1 = 498.