How to Identify Successor and Predecessor in Maths with Examples
“Honourable Mr. Narendra Modi is the 14th Prime Minister of the Republic of India. His predecessor was Dr. Manmohan Singh.”
We often see this sentence in our History or Social Studies books. But what does the term “predecessor” mean? Today, we will learn about successor and predecessor meanings and how to find them.
Predecessors and Successors: What are They?
In Mathematics, the terms predecessor and successor are used almost always in context with another given whole number. In general terms, the predecessor or successor to a person or an object is that which comes before or after it, respectively. For example, ‘the king’s son was chosen to be his successor’ implies that after the king, his son would rule after him.
While on the other hand, "Pandit Jawaharlal Nehru was Lal Bahadur Shastri's predecessor as the prime minister of independent India." This implies that prior to Lal Bahadur Shastri's term as the Prime minister of Independent India, Pandit Jawaharlal Nehru was the prime minister in charge of the affairs of India and her people.
What is Predecessor?
So what is the predecessor in mathematical terms? The predecessor is the number that “precedes” or comes before the given number. Simply put, the predecessor of a number is one less than it. Some examples of predecessors are-
The predecessor of 1 is 0.
The predecessor of 22 is 21.
The predecessor of 99 is 98.
For example, if “b” is the given value, then the predecessor of the given value (b) is the value “a”.
How Do We Find the Predecessor?
The formula to derive the predecessor is $(n-1)$ where $n$ is the given value, and one is subtracted to show the predecessor of that number.
Hence the formula to derive the predecessor: Predecessor $=n-1$
What is Successor?
Now that we have learned what the predecessor is, what is the successor in mathematics? The successor is the number that “succeeds” or comes after the given number. In simple terms, the successor of a number is one more than it. Some examples of successors are-
The successor of 1 is 2
The successor of 22 is 23
The successor of 99 is 100
For example, if the given value is 'b', then the successor of the given value (b) is the value 'c'.
How Do We Find the Successor?
The formula to derive the successor is: ( n + 1 ) where n is the given value, and one is added to gain the successor of that number.
Hence the formula to derive the successor: Successor = n + 1
Example of Successor and Predecessor
Solved Examples
1. Find the predecessor for the following numbers:
1000
20
345
Ans: The predecessors of the numbers are:
(1000-1) = 999
(20-1) = 19
(345-1) = 344
2. Find the successors for the following numbers:
20
9999
4
Ans: The successors of the numbers are:
(20 + 1) = 21
(9999 + 1) = 10000
(4 + 1) = 5
Practice Questions
1. If the given value is 99999, what is its successor? Upon deriving the answer, find the successor to the derived value as well.
2. The given value is 120. Find the predecessor of the given value. Also, find the predecessor of the answer.
Answers:
1. Successor 1= 100000; Successor 2= 100001
2. Predecessor 1= 119; Successor 2= 118
Summary
To sum up, what we have learned so far:
The term predecessor refers to the number that precedes or comes before the given number.
The term successor refers to the number that succeeds or comes after the given number.
The formula to find the predecessor is: Predecessor = n - 1.
The formula to find the successor is: Successor = n + 1.
All whole numbers, upon using the formulae, may produce their respective successors and predecessors.
A predecessor for the number zero is not possible, but its successor is 1.
FAQs on Successor and Predecessor Numbers Explained
1. What is a successor in mathematics?
Successor in mathematics is the number that comes immediately after a given number when counting. For example, the successor of 7 is 8. You can always find the successor by adding 1 to the original number: $n + 1$.
2. What does predecessor mean in numbers?
A predecessor is the number that comes just before another number. For example, the predecessor of 10 is 9. You find it by subtracting 1 from the given number: $n - 1$.
3. How do you find the successor and predecessor of a number?
To calculate the successor and predecessor of a number:
- Successor: Add 1 ($n + 1$)
- Predecessor: Subtract 1 ($n - 1$)
4. Is zero the successor or predecessor of one?
Zero is the predecessor of one. In whole numbers, if you subtract 1 from 1 ($1 - 1 = 0$), you get zero. So, zero comes just before one on the number line, making it its predecessor.
5. Can every number have a successor and a predecessor?
In counting numbers (natural numbers), every number has a successor. However, only numbers greater than 1 have a predecessor. Zero does not have a predecessor among natural numbers, but all whole numbers have both.
6. Why is finding the successor and predecessor important in mathematics?
Successor and predecessor concepts help understand number order, counting, and arithmetic operations. They build a strong foundation for
- comparing numbers
- performing addition or subtraction
- learning about sequences and patterns
7. What is the successor of 999?
The successor of 999 is 1000. When you add 1 to 999 ($999 + 1 = 1000$), you get the next number, which is the successor in the number sequence.
8. What is the predecessor of 500?
The predecessor of 500 is 499. You simply subtract 1 from 500 ($500 - 1 = 499$) to find which number comes just before 500 in the counting order.
9. How do successor and predecessor work on a number line?
On a number line:
- Successor is the number to the right
- Predecessor is the number to the left
10. Can negative numbers have successors and predecessors?
Yes, negative numbers also have both successors and predecessors. For example, the successor of $-4$ is $-3$ ($-4 + 1$), and the predecessor is $-5$ ($-4 - 1$). This applies across the set of integers.
11. How do successor and predecessor relate to whole numbers?
In whole numbers (0, 1, 2, ...), every number has a successor, but only numbers greater than zero have a predecessor. Zero is the smallest whole number and does not have a predecessor within whole numbers.
12. How is the successor of a number different from its square?
The successor of a number is found by adding 1. The square is found by multiplying the number by itself ($n \times n$). For example, for 3, the successor is 4, but the square is 9.
