Table of Contents
Have you ever wondered about numbers that come just before or after a given number? These special numbers have names – they are called “predecessors” and “successors.” But, what are the Successor and Predecessor in Math? In this blog, we’ll dive into what these terms mean, explore examples, and learn how to find them
What are the Successor and Predecessor in Math?
In mathematics, a successor function is a function that maps a natural number n to the next natural number, n + 1. The successor function is also called the natural number function, or the counting function.
The predecessor function is a function that maps a natural number n to previous natural number, n – 1.
What is a Successor?
A successor is the number that comes right after a given number. Going back to our stepping stones analogy, the successor is the stone you’re about to step onto. For instance, the successor of 7 is 8, as it comes immediately after 7.
Examples of Successors
- Successor of 14: 15
- Successor of 32: 33
- Successor of -3: -2 (again, when dealing with negative numbers)
What is a Predecessor?
On the flip side, a predecessor is the number that comes just before a given number. Imagine numbers as stepping stones – the predecessor is the stone just before the one you’re standing on. For example, the predecessor of 5 is 4, as it comes right before 5.
Examples of Predecessors
- Predecessor of 10: 9
- Predecessor of 22: 21
- Predecessor of 0: -1 (when dealing with negative numbers)
Predecessor and Successor of Integers
In the world of numbers, every integer has a neighbor on its left and another on its right. These neighbors are called the predecessor and successor, respectively. Predecessor is the integer that comes just before a given number, while successor is the integer that comes right after it.
Examples:
- For the integer 7, the predecessor is 6, and the successor is 8.
- For the integer -5, the predecessor is -6, and the successor is -4.
This concept isn’t limited to positive integers. It extends to negative integers and zero as well. For instance, the predecessor of -3 is -4, and the successor of -7 is -6.
To find the predecessor of a number, subtract 1 from it. To find the successor, simply add 1. This works like taking steps on a number line, either to the left for predecessor or to the right for successor.
Keep in mind that predecessor and successor are like close companions to each integer, creating a neat order along the number line.
Here’s the information presented in a tabular format:
| Integer | Predecessor | Successor |
|---|---|---|
| 7 | 6 | 8 |
| -5 | -6 | -4 |
| -3 | -4 | -2 |
| 0 | -1 | 1 |
| 12 | 11 | 13 |
| -8 | -9 | -7 |
Remember, the predecessor is the integer to the left of the given number, while the successor is the integer to the right. This pattern holds for both positive and negative integers, as well as zero.
How to Find the Predecessor and Successor of a Given Number?
Finding successors and predecessors of integers is quite simple. Here’s how you can do it:
Finding the Successor:
- Take the given integer.
- Add 1 to the given integer to find its successor.
- The result is the successor of the given integer.
Finding the Predecessor:
- Take the given integer.
- Subtract 1 from the given integer to find its predecessor.
- The result is the predecessor of the given integer.
For example:
- To find the successor of 7, add 1 to 7, which gives 8.
- To find the predecessor of -5, subtract 1 from -5, which gives -6.
It’s a simple process that works for both positive and negative integers.
Difference Between Successor and Predecessor
| Aspect | Successor | Predecessor |
|---|---|---|
| Definition | The number that comes after a given integer. | The number that comes before a given integer. |
| Calculation | Add 1 to the given integer. | Subtract 1 from the given integer. |
| Example | Successor of 5 is 6. | Predecessor of 9 is 8. |
| Symbolic Representation | n + 1 | n – 1 |
| Use | Used in counting, progression, etc. | Used in calculations, counting in reverse, etc. |
Frequently Asked Questions (FAQs) about Predecessors and Successors
Predecessor is the number that comes just before a given number, while successor is the number that comes right after it.
To find the successor, add 1 to the given number. To find the predecessor, subtract 1 from the given number.
Yes, they work for negative numbers too. For negative integers, the rules remain the same – predecessor is the smaller negative number, and successor is the larger negative number.
The predecessor of 8 is 7, and the successor of 12 is 13. Similarly, the predecessor of -3 is -4, and the successor of -9 is -8.
The main difference lies in their positions on the number line. Predecessor moves backward, while successor moves forward. It's like taking steps left or right on the line.
No, the names are not unique for each number. For instance, the predecessor of 6 is simply 5, and the successor of 6 is just 7.
In the case of the number 0, its predecessor is -1, and its successor is 1.
Think of a number line as a path. If you're standing on a number, the predecessor is behind you, and the successor is ahead of you, just like footsteps on a trail. What is a predecessor and successor in numbers?
How do I find the predecessor and successor of a number?
Do predecessors and successors work for negative numbers?
Can you provide examples of predecessors and successors?
What's the difference between a predecessor and a successor?
Do predecessors and successors have specific names for each number?
Are there any exceptions when finding predecessors and successors?
Can you give an analogy for understanding predecessors and successors?
