In mathematics, Predecessor and Successor are terms used to describe numbers that come before and after a given number. For example, the successor of 2 is 3, and the predecessor of 2 is 1. Predecessor and Successor are important terminologies used in mathematics as well as computer science.
In this article, we will discuss both Predecessor and Successor in detail including their definitions, examples as well as methods to find Predecessor and Successor.
What is a Predecessor in Maths?
The predecessor is the number that comes immediately before the given number or a number that precedes another number in any series or while counting.
For natural numbers or integers, the predecessor of any given number is one less than the provided number. In the context of number lines or when discussing numbers in order, the term “predecessor” is commonly used to describe the number that comes before the given number.
Predecessor Definition
A predecessor is a number that appears right before a given value within sequence, In other words also, if ‘n’ is a positive integer, then n−1 is the past of n.
Examples of Predecessor
So, Let’s look at some of the examples given below;
- The predecessor of 5 is 4 because 4 comes just before 5 when counting: 4, 5.
- The predecessor of 20 is 19 because 19 comes just before 20 when counting: 19, 20.
- The predecessor of -3 is -4 because -4 comes just before -3 when counting: -4, -3.
What is a Successor in Maths?
The successor is the number that comes after the given number, or a number that succeeds another number in any sequence or while counting.
In the context of number lines or when discussing numbers in order, the term “successor” is commonly used to describe the number that comes after the given number.
Successor Definition
A successor is a number that appears right after a given value within sequence, In other words also, if ‘n’ is a positive integer, then n+1 is the progress of n.
Even, It can be said that a counting number is an increasing order or following a pattern of forward counting, which comes right after the designated number.
Examples of Successor
So, Let’s look at some of the examples given below;
- The successor of 5 is 6 because 6 comes just after 5 when counting: 5, 6.
- The successor of 20 is 21 because 21 comes just after 20 when counting: 20, 21.
- The successor of -3 is -2 because -2 comes just after -3 when counting: -3, -2.
How to Find Predecessor and Successor?
Each integer has only one successor and one predecessor, where the successor is on the right side of the number line and the predecessor is on the left side of the number line. Therefore, the given whole number is 2, a predecessor of 2 is 1 and a successor of 2 is 3.
We add 1 to any integer and subtract 1 from any integer to find its successor and predecessor respectively i.e.,
- To find Successor of any Integer we can use the formula i.e., S(n) = n + 1. Where n is the number for which successor is required.
- To find Predecessor of any Interger we can use the formula i.e., P(n) = n – 1. Where n is the number for which predecessor is required.
How to Find the Predecessor of Integer?
To find the predecessor of any integer we can use the formulas discuss below:
Predecessor = Given Number – 1 i.e., n – 1
Where n is the given number.
For example, If you want to find the predecessor of 22, you would precede it by subtraction
i.e., Predecessor = Given Number – 1 = 22 – 1 = 21
Similarly, If you have any other whole number, you can apply the same formula for precedes one less than the given number in the sequence.
How to Find the Successor of any number?
To find the sucessor of any integer we can use the formulas discuss below:
Successor = Given Number + 1 i.e., (n+1)
Where n is the given number.
For example, If you want to find the Successor of 22, you would succeed it by Addition:
Successor = Given Number + 1 = 22 + 1 = 23.
Similarly, If you have any other whole number, you can apply the same formula for Succeeding one more than the given number in the sequence.
Successor Vs Predecessor
- Successor: The successor of a number is the number that comes immediately after it in a numerical sequence.
- For example, in natural number 3 is successor of 2.
- Predecessor: The predecessor of a number is the number that comes immediately before it in a numerical sequence.
- For example, in integer -1 is predecessor of 0.
Difference Between Successor and Predecessor
Some of the key differences between Successor and Predecessor are listed in the following table:
| The successor of a number is the number that comes immediately after it in the sequence. |
The predecessor of a number is the number that comes immediately before it in the sequence. |
| The successor of 5 is 6, as it comes immediately after 5. |
The predecessor of 5 is 4, as it comes immediately before 5. |
| Successor = Number + 1 |
Predecessor = Number – 1 |
| In a sequence, the successor of an element is the element that follows it. |
In a sequence, the predecessor of an element is the element that precedes it. |
Read More,
Solved Questions on Predecessor and Successor
Question 1: How the successor is different from the predecessor?
Answer:
The successor of a number is the immediate next number obtained by adding 1, while the predecessor is the immediate previous number generated by subtracting 1. Whereas, they represent the after and before movement in a numerical sequence.
Question 2: Find the Predecessor of a 1000.
Answer:
To find the predecessor of 1000, you subtract 1 from 1000:
Predecessor of 1000 = 1000 – 1 = 999
Therefore, the predecessor of 1000 is 999.
Question 3: A two-digit number’s successor can be a three-digit number. Justify this statement.
Answer:
Yes, the successor of a two-digit number can be a three-digit number, as adding 1 to the highest two-digit number (99) will be 100, Therefore, 100 is a three-digit number.
Question 4: Find the Successor of an 11999.
Answer:
To find the Successor of a 11999, you Add 1 with 11999.
Successor of 11999= 11999+1 = 12000
Therefore, the successor of 11999 is 12000.
Question 5: Do zero has a predecessor?
Answer:
No, zero (0) does not have a predecessor in the context of natural numbers. But in context to integers 0 has a predecessor i.e., -1.
Question 6: Write the predecessor and successor of the number 25.
Answer:
To find the predecessor of 25, subtract 1 from 25 i.e.,
Predecessor of 25 = 25 – 1 = 24.
To find the successor of 25, add 1 to 25:
Successor of 25 = 25 + 1 = 26.
So, the predecessor of 25 is 24, and the successor of 25 is 26.
Predecessor and Successor: Practice Questions
Q1: Find the Successor of a 119.
Q2: Find the Predecessor of a 2229.
Q3: Give at least two examples of Predecessors.
Q4: Give at least two examples of Successor.
Predecessor and Successor: FAQs
1. What is an Example of a Predecessor?
One example of the predecessor of 5 is 4.
2. What are the Predecessor and Successor for 6000?
- Predecessor of 6000: 5999
- Successor of 6000: 6001
3. What is Predecessor of 94?
Predecessor of 94 is 93.
4. What is Successor of 99?
Successor of 99 is 100.
5. What is Predecessor of 0?
In the set of natural numbers, 0 has no predecessor. In integers, the predecessor is -1.
6. What is Successor of -5?
Sucessor of -5 is -4.
7. Write Predecessor of 1.
In natural numbers, it’s 0. In integers, it’s also 0.
8. What is Peano Axioms?
These are axioms for the natural numbers proposed by Giuseppe Peano. They define the basic properties of natural numbers, like 0 being a natural number, each number having a unique successor, and the principle of mathematical induction.
Share your thoughts in the comments
Please Login to comment...