Definition Formula And Solved Examples Of Successor And Predecessor
The concept of successor and predecessor in maths plays a key role in mathematics and helps students understand the order and relationship among numbers. It's a topic that regularly appears in tests, worksheets, and even in real-life scenarios such as counting objects, arranging things, and coding.
What Is Successor and Predecessor in Maths?
A successor in maths is the number that comes immediately after a given number, while a predecessor is the number just before it. For example, in the sequence 7, 8, 9, the successor of 8 is 9, and the predecessor of 8 is 7. You’ll find this concept applied in areas such as counting numbers, sequencing in coding, and calendar dates.
Key Formula for Successor and Predecessor in Maths
Here’s the standard formula that always works for whole numbers:
- Successor of a number = Number + 1
- Predecessor of a number = Number – 1
Why Is Successor and Predecessor Important?
Successor and predecessor in maths are the building blocks of number sense for children. These concepts make it easier for students to understand counting, perform quick mental addition and subtraction, and recognize number patterns. Recognizing before/after relationships in numbers also helps with problem-solving in exams and daily activities.
Step-by-Step Examples
| Number | Successor | Predecessor |
|---|---|---|
| 15 | 16 | 14 |
| 1000 | 1001 | 999 |
| 43 | 44 | 42 |
| 0 | 1 | Not defined for whole numbers |
Worked Out Problem
Question: Find the successor and predecessor of 99999.
1. Given number = 999992. Successor = 99999 + 1 = 100000
3. Predecessor = 99999 – 1 = 99998
Answer: Successor is 100000, Predecessor is 99998.
Successor and Predecessor with Negative Numbers
For integers, the rule of successor (+1) and predecessor (-1) works for both positive and negative numbers. With negative numbers, the successor of –3 is –2, and the predecessor of –3 is –4. However, in the set of natural numbers (1, 2, 3, ...), there is no predecessor for 1, and in whole numbers (0, 1, 2, ...), there is no predecessor for 0.
Real-Life Use Cases & Fun Facts
You see successor and predecessor in maths in action when you:
- Turn the calendar from one day to the next (successor: today + 1 day = tomorrow)
- Check seat numbers (if you are in seat 7, your predecessor sat in seat 6, and your successor will sit in 8)
- Program loops in computer science (next/previous step)
Fun Fact: In Peano’s axioms, the concept of “successor” builds up the entire number system!
Try These Yourself
- What is the successor of 250?
- Find the predecessor of 1200.
- Is there a predecessor for 0 in whole numbers?
- Give the successor and predecessor for –5.
Frequent Errors and Misunderstandings
- Writing the same number as both successor and predecessor.
- Applying the concept to fractions or decimals incorrectly (the next/previous is not always just ±1 for non-integers).
- Forgetting zero has no predecessor in whole numbers.
Relation to Other Number Concepts
The idea of successor and predecessor is strongly linked with number line ordering, even & odd numbers, and arithmetic operations. Understanding this helps with learning addition, subtraction, and comparing numbers. For more on ordering and comparing, try our Greater Than Less Than Calculator.
Classroom Tip
A quick way to remember how to find a successor is to think "add one" to the number, and for predecessor, "subtract one." Vedantu’s experienced teachers often use number lines and simple drawing tricks to make this concept visual and easy in live classes.
More Practice: Worksheets and Activities
Practice is key for mastering successor and predecessor. Download printable worksheets or try online quizzes aligned with CBSE and NCERT standards to test your knowledge. You can also use the Math Basic Calculator for quick checks!
Useful Internal Links for More Learning
- Numbers to Words Converter
- Long Addition Calculator
- Rounding Numbers Tool
- Comparing Fractions Calculator
We explored successor and predecessor in maths — from clear definitions, formulas, and real-life examples, to helpful tricks and links for extra practice. Keep practicing with Vedantu and you’ll soon be a pro at finding successors and predecessors for any number!
FAQs on What Are The Successor And Predecessor In Mathematics
1. What is the successor of a number?
The successor of a number is the number that comes immediately after it when 1 is added. In simple terms, the successor of any number n is n + 1.
- Successor of 5 = 5 + 1 = 6
- Successor of 100 = 100 + 1 = 101
- Successor of -3 = -3 + 1 = -2
2. What is the predecessor of a number?
The predecessor of a number is the number that comes immediately before it when 1 is subtracted. In general, the predecessor of any number n is n - 1.
- Predecessor of 9 = 9 - 1 = 8
- Predecessor of 50 = 50 - 1 = 49
- Predecessor of 0 = 0 - 1 = -1
3. How do you find the successor and predecessor of a number?
To find the successor, add 1 to the number, and to find the predecessor, subtract 1 from the number.
- Step 1: Take the given number (for example, 25).
- Step 2: Add 1 → 25 + 1 = 26 (successor).
- Step 3: Subtract 1 → 25 - 1 = 24 (predecessor).
4. What is the formula for successor and predecessor?
The formula for successor is n + 1 and for predecessor is n - 1, where n is any number. These formulas apply universally in arithmetic and number systems.
- If n = 200, successor = 201
- If n = 200, predecessor = 199
5. What is the successor and predecessor of 0?
The successor of 0 is 1 and the predecessor of 0 is -1. Using the formulas:
- Successor = 0 + 1 = 1
- Predecessor = 0 - 1 = -1
6. What is the difference between successor and predecessor?
The successor is one more than a number, while the predecessor is one less than a number. The key difference lies in the operation used.
- Successor → Add 1
- Predecessor → Subtract 1
- Example (10): Successor = 11, Predecessor = 9
7. Can a negative number have a successor and predecessor?
Yes, every negative number has both a successor and a predecessor. The same rules apply: add 1 for successor and subtract 1 for predecessor.
- For -5: Successor = -5 + 1 = -4
- For -5: Predecessor = -5 - 1 = -6
8. What is the successor and predecessor on a number line?
On a number line, the successor is the number immediately to the right, and the predecessor is the number immediately to the left. Movement direction determines the result.
- Move one step right → Successor
- Move one step left → Predecessor
- Example: From 3, right → 4, left → 2
9. What is the successor and predecessor of a large number?
The successor of a large number is found by adding 1, and the predecessor is found by subtracting 1. The size of the number does not change the rule.
- For 9,99,999: Successor = 10,00,000
- For 9,99,999: Predecessor = 9,99,998
10. Why are successor and predecessor important in Maths?
Successor and predecessor are important because they help in understanding number sequence, ordering of numbers, and basic arithmetic operations. They form the foundation of counting and number systems.
- Used in comparing numbers
- Helpful in solving integer problems
- Essential for understanding ascending and descending order
