Predecessor and Successor: Definitions, and Examples

Let us go back to those school days when your teacher started teaching you counting and backward counting. Remember? While teaching counting, your teacher taught you a technique to find the successor of the previous number and while teaching you backwards counting, you have been taught to find the predecessor of the previous number. To find a number’s successor, add one to that number, whereas to find the predecessor of a number, subtract one from the given number.

In Math, the terms successor and predecessor refer to numbers that come directly after or before a certain number. Both Predecessor and Successor were essentially only applicable to entire numbers. After numbers refer to the successor, whereas before numbers refer to the predecessor.

In this article, we will discuss more about the successor and predecessor and reach the zenith of understanding the concept.

Predecessor and Successor

To understand the concept of predecessor and successor, let’s go back to the history of India.

Akbar the great was one of the elite rulers of India. Akbar’s father name was Humayun, and his son’s name was Jahangir. Now, Humayun was the predecessor of Akbar, and Jahangir was the successor of Akbar.

Sounds confusing?

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Alright, let us give it another try while taking the examples of fruits.

Look at the figure given below.

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Here, we can see that banana, orange, apple, and strawberry are arranged in a queue.

From the figure, we can tell that apple is placed after strawberry, and thus, we can say that apple is the successor of strawberry. Similarly, orange is placed after apple, and therefore, orange is the successor of apple.

Again, if we look at the figure, we can see that orange is placed before the banana, and thus, we can say that orange is the predecessor of the banana. Similarly, strawberry is placed before apple, and hence, we can say that strawberry is the predecessor of apple.

Here’s another example. Let us understand with the help of numbers.

Let us note down the counting numbers from \(1\) to \(10\) as shown in the figure.

Taking the number \(6\) into consideration, we can see that \(5\) comes before \(6\) and \(7\) comes after \(6\)

Therefore, we can say that the number that comes before the given number is known as the predecessor of that number. Likewise, the number that comes after the given number is known as the successor of the given number.

Suppose we take the example of the first three whole numbers, which are \({\rm{1,}}\,{\rm{2,}}\,{\rm{3}}\) We can say \(1\) is the predecessor of \(2\) and \(3\) is the successor of \(2\).

Let’s give it a try with a slightly bigger number. Let’s find the predecessor and successor of \({\rm{100}}\)

The predecessor of \({\rm{100}}\,{\rm{ = }}\,{\rm{100 – 1 = 99}}\) and successor \({\rm{100}}\,{\rm{ = }}\,{\rm{100  + }}\,{\rm{1 = 101}}\).

The predecessor and successor of \({\rm{100}}\,\) are shown in the below figure.

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Predecessor and Successor of Larger Numbers

The same concept is also applied to the larger numbers when we have to find its predecessor or the successor.

A predecessor is a number that precedes the given number or comes before the given number whereas, a successor is a number that succeeds the given number or comes after the given number.

For example,

The predecessor of \({\rm{10,000}}\,is\,10,000 – 1 = 9,999\)

The predecessor of \(55,\,590\,\,is\,55,590 – 1 = 55,589\)

The predecessor of \(20,\,160\,\,is\,20,160 – 1 = 20,159\)

Similarly,

The successor of \({\rm{19,999}}\,is\,19,999 + 1 = 20,000\)

The successor of \(50,\,000\,\,is\,50,000 + 1 = 50,001\)

The successor of \(99,\,999\,\,is\,99,999 + 1 = 1,00,000\)

Predecessor and Successor of Integers

So far, we have learned only to find the predecessor and successor of whole numbers.

Let us understand the concept of predecessor and successor in integers as well.

But before that, let’s have a look at what integers are.

Integers can be defined as the set of natural numbers and their additive inverse, including zero. The set of integers is \(\left\{ {…\,\,.. – 3, – 2, – 1,0,1,2,3…\,\,..} \right\}\)Integers are numbers that cannot be a fraction or decimal.

Integers are basically an extension of whole numbers and natural numbers.

That is,

Whole Numbers \( + \) Negative Natural numbers \( = \) Integers

Natural Numbers \( + \) Zero \( + \) Negative Natural Numbers \( = \) Integers

Thus, integers are a collection of positive numbers, negative numbers, and zero.

The predecessor of \( – 1\) will be \( – 1 – 1 =  – 2\)

Similarly, the predecessor of \( – 2 =  – 2 – 1 =  – 3\)

The successor of\( – 3 =  – 3 + 1 =  – 2\)

Let us summarize the predecessor and successor of\( – 3\) in one number line.

When we consider our number line for integers, as we move forward with each step to the right, we are getting the successor of each previous integer. In the same way, when we move forward to the left, we get the predecessor of each number.

Predecessor and Successor Examples

Let us be more efficient in finding the predecessor and successor of numbers with the help of more examples.

Example: Find the predecessor of the following given numbers.

a) \(80,000\)
b) \( – 4190\)
c) \(39,999\)
d) \(1,000\)
e) \( – 1,000\)

The predecessor of the given numbers are as follows:

1. The predecessor of \(80,000\) is \(80,000 – 1 = 79,999\)
2. The predecessor of \( – 4190\) is \( – 4190 – 1 =  – 4191\)
3. The predecessor of \(39,999\) is \(39,999 – 1 = 39,998\)
4. The predecessor of \(1,000\) is \(1,000 – 1 = 999\)
5. The predecessor of \( – 1,000\) is \( – 1,000 – 1 =  – 1,001\)

Example: Find the successor of the following given numbers.

a) \(1,23,999\)
b)\( – 999\)
c)\(9\)
d)\(36,689\)
e)\( – 109\)

The successor of the given numbers are as follows:

1. The successor of \(1,23,999\,is\,1,23,999\, + 1 = 1,24,000\)
2. The successor of \( – 990\,is – 990 + 1 =  – 989\)
3. The successor of \(9\,is\,9 + 1\, = 10\)
4. The successor of \(36,689\,is\,36,689 + 1 = 36,690\)
5. The successor of \( – 109\,is\, – 109\, + 1 =  – 108\)

Solved Examples

Q.1. What is the predecessor and successor of \(999\)?
Ans: According to the definition of the predecessor, we have to subtract \(1\) from the given number, and to find the successor, we have to add \(1\).Thus,
The predecessor of \(999\) will be \(999 – 1 = 998\)
and the successor of \(999\) will be \(999 + 1 = 1000\)

Q.2. Find the predecessor of the following given numbers.
a)200 b)657 c)350 d)601
Ans: The predecessor can be found out by subtracting \(1\) from the given number.
1. The predecessor of \(200\) is \(200 – 1 = 199\)
2. The predecessor of \(657\) is \(657 – 1 = 656\)
3. The predecessor of \(350\) is \(350 – 1 = 349\)
4. The predecessor of \(601\) is \(601 – 1 = 600\)

Q.3. Find the successor of the following given numbers.
a) \(401\) b) \(657\) c) \(649\) d)\(555\)
Ans: The successorcan be found out by adding \(1\) to the given number.
1. The successor of \(401\) is \(401 + 1 = 402\)
2. The successor of \(401\) is \(401 + 1 = 402\)
3. The successor of \(401\) is \(649 + 1 = 650\)
4. The successor of \(401\) is \(555 + 1 = 556\)

Q.4. Find the predecessor of the following negative integers.
\(a)\;-300\;\;\;\;\;b)\;-21\;\;\;\;c)\;-149\;\;\;d)\;-199\)
Ans: The predecessor can be found out by subtracting \(1\) from the given number.
1. The predecessor of \(-300\) is \(-300 – 1 = -301\)
2. The predecessor of \(-21\) is \(-21 – 1 = -22\)
3. The predecessor of \(-149\) is \(-149 – 1 = -150\)
4. The predecessor of \(-199\) is \(-199 – 1 = -200\)

Q.5. Find the successor of the following negative integers.
a)\(-111\) b) \(-59\) c) \(-300\) d)\(-2\)
Ans: The successor can be found out by adding \(1\) to the given number.
1. The successor of\(-111\) is \(-111 + 1 = -110\)
2. The successor of\(-59\) is \(-59 + 1 = -58\)
3. The successor of\(-300\) is \(-300 + 1 = -299\)
4. The successor of\(-2\) is \(-2 + 1 = -1\)

Summary

In this article, we learned the definitions of the predecessor and the successor. We also learned the method to find the predecessor and the successor of a number. In addition to this, we had a quick brief description of integers and then, with the help of examples, learned to find the predecessor and successor of negative numbers as well. We applied the concept of finding the predecessor and successor to the larger numbers too.

Frequently Asked Questions (FAQs)

We have provided some frequently asked questions about predecessor and successor here:

Q.1. What is the successor of \(3\)?
Ans: The successor of \(3\) can be found by adding \(1\) to the given number. Hence, the successor of \(3\) is \(3 + 1 = 4\)

Q.2. What are the predecessor and the successor of \(49,999\)?
Ans: The predecessor of \(49,999\,is\,49,999 – 1 = 49,999\) and the successor of \(49,999\) is \(49,999 + 1 = 50,000\)

Q.3. What is the successor of \(9999\)?
Ans: As per the definition, successor of a number is obtained when we add \(1\) to the given number. Hence, the successor of \(9999\) is \(9999 + 1 = 10000\)

Q.4. What is the predecessor of \(45\)?
Ans: The predecessor of\(45\) will be\(1\) less than\(45\) Thus, the predecessor of \(45 = \,45 – 1 = 44\)

Q.5. Define predecessor and successor with examples.
Ans: The number that comes just before the given number is known as the predecessor of that number. The number that comes just after the given number is known as the successor of the given number.
Suppose we take the example of the first three whole numbers, which are \(1,2,3.\) So we can say that \(1\) is the predecessor of \(2\) and \(3\) is the successor of \(2\).

Q.6. What is the predecessor of \(399\)?
Ans: The predecessor of a number can be found out by subtracting \(1\) from \(399\) Thus, the predecessor of \(399\) is \(399 – 1 = 398\).

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