Predecessor and Successor 

In Mathematics, the two terms commonly used for sequences and series of whole numbers are Successor and Predecessor.

• Successor is defined as the number that comes immediately after a given number.
• Predecessor is defined as the number that comes immediately before a given number.

In this article, we will discuss the concepts of successors and predecessors in detail.

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What are the Predecessor and Successor

In mathematics, the terms successor and predecessor refer to numbers that directly follow or precede another number. These concepts are particularly relevant for whole numbers.

• Successor: The number that comes immediately after a given number. To find the successor, simply add one to the number. For example, the successor of 7 is 7+1=8.
• Predecessor: The number that comes immediately before a given number. To find the predecessor, subtract one from the number. For example, the predecessor of 7 is 7−1=6.

Meaning of Successor

A successor is a term that comes immediately after a given number, term, or value. For example, if n is a whole number, then the successor of n is n+1. Other terms used for a successor include “just after,” “immediately after,” and “next number” or “next value.”

Successor Examples

If n = 6, then successor of 6 is 6 + 1 = 7

If n = 12, then successor of 12 is 12 + 1 = 13

If n = 22, then successor of 22 is 22 + 1 = 23

If n = 55, then successor of 55 is 55 + 1 = 55

If n = 125, then successor of 125 is 125 + 1 = 126

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Meaning of Predecessor

A predecessor refers to a value that occurs immediately before a certain number or term. If x is any given whole number, its predecessor is x−1. To calculate the predecessor of any number, simply subtract 1 from it.

Example of Predecessor

If x = 6, then predecessors 6 is 6 – 1 = 5

If x = 12, then the predecessors of 12 is 12 – 1 = 11

If x = 22, then predecessors of 22 is 22 – 1 = 21

If x = 55, then predecessors of 55 is 55 – 1 = 54

If x = 125, then predecessors of 125 is 125 – 1 = 124

Examples of Predecessor and Successor

Let’s consider the number 18. Its successor is 19, and its predecessor is 17. Similarly, if the given number is 226, the successor would be 227, and the predecessor would be 225. Furthermore, if x is the successor of y, then y is the predecessor of x. For example, since 80 is the successor of 79, 79 is the predecessor of 80.

Role of whole numbers

Successor and predecessor only apply to whole numbers, which include zero, one, two, three, and so on. These concepts do not apply to negative numbers, fractions, or decimals. Importantly, every whole number has a successor. However, with the exception of zero, every whole number also has a predecessor.

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How to Find Successors and Predecessors?

Successors and predecessors are essential concepts used in mathematics and physics. Below are steps to find the Predecessor and Successor :

Finding the Successor: The successor of a given number is found by adding 1 to the number. For example:

• The successor of 0 is 1.
• The successor of 1 is 2.
• The successor of 2 is 3.

Every whole number has its successor.

Finding the Predecessor: The predecessor of a given number is found by subtracting 1 from the number. For example:

• The predecessor of 1 is 0.
• The predecessor of 2 is 1.
• The predecessor of 3 is 2.

However, the whole number 0 does not have a predecessor. Therefore, every whole number except 0 has its predecessor.

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Difference Between Successor and Predecessor

The table given below mentions the Difference Between Successor and Predecessor.

Concept	Definition	Formula	Example
Successor	The number following the given number	Successor = Given number + 1	Successor of 56 → 57
Predecessor	The number preceding the given number	Predecessor = Given number – 1	Predecessor of 54 → 53

The predecessor and successor on a Number line

The successor of a number is the number that comes immediately after it on the number line.

Direction: Moving in a forward direction or to the right.

Example: If the current number is 6, the successor is 7.

This means 7 is directly after 6 on the number line.

Whereas, the predecessor of a number is the number that comes immediately before it on the number line.

Direction: Moving in a backward direction or to the left.

Example: If the current number is 4, the predecessor is 3.

This means 3 is directly before 4 on the number line.

Successor:

5 → 6 → 7

Here, 6 is the successor of 5.

Predecessor:

4 → 3 → 2

Here, 3 is the predecessor of 4.

Therefore, on a number line, the successor is always to the right of the given number, while the predecessor is always to the left. Whole numbers are always positive or zero and follow this straightforward sequence on the number line.

Important notes

Below are a few key points related to the Predecessor and Successor.

• Successors and predecessors are strictly defined for whole numbers (0, 1, 2, 3, …). They do not extend to fractions, decimals, or negative integers.
• Zero has no predecessor. Every other whole number has both a successor and a predecessor.
• The concepts of successor and predecessor are not relevant to fractional or decimal values.

Solved Examples: Predecessor and Successor

Problem: Find the successor of the number 12.

Solution: To find the successor of a number, add 1 to it.

For the number 12: Successor=12+1=13

Answer: The successor of 12 is 13.

Problem: Find the predecessor of the number 25.

Solution: To find the predecessor of a number, subtract 1 from it.

For the number 25: Predecessor=25−1=24

Answer: The predecessor of 25 is 24.

Problem: What is the successor of 0?

Solution: To find the successor, add 1 to the number.

For the number 0: Successor=0+1=1

Answer: The successor of 0 is 1.

Problem: Find the predecessor of the number 1.

Solution: To find the predecessor, subtract 1 from the number.

For the number 1: Predecessor=1−1=0

Answer: The predecessor of 1 is 0.

Practice Questions: Predecessor and Successor

1. What is the successor of 87?
2. What is the predecessor of 34?
3. What is the successor of 0?
4. Find the predecessor of 100.
5. Given the sequence 22, 23, 24, find the successor and predecessor of 23.
6. What are the successor and predecessor of 1,500,000?
7. What is the successor of 999,999?
8. Find the predecessor of 8.7.
9. If John has 45 apples, what is the number of apples if he gains one more?
10. Sarah is planning to give 73 candies to her friends. What is the number of candies she has if she gave away one less?
11. For the sequence 15, 16, 17, 18, identify the successor and predecessor of 16.

FAQs: Predecessor and Successor

What is a successor in mathematics?

In mathematics, a successor of a number is the number that comes immediately after the given number. For whole numbers, the successor is found by adding 1 to the given number. For example, the successor of 7 is 8, and the successor of 15 is 16.

How do you find the predecessor of a number?

The predecessor of a number is the number that comes immediately before it. To find the predecessor of a whole number, subtract 1 from the given number. For instance, the predecessor of 12 is 11, and the predecessor of 23 is 22.

Can the concepts of successor and predecessor be applied to fractions and decimals?

No, the concepts of successor and predecessor apply only to whole numbers. Successor and predecessor refer to numbers that are directly next to or before a given whole number. Fractions and decimals do not have successors or predecessors in the same manner, as their sequence involves infinitely many values between any two given numbers.