Is there any natural number which has no successor? Is there a last number?
Answer
363.9k+ views
Hint: In this question, we need to first look at the definition of successor; it gives us a clear picture of how to answer. We need to know about natural numbers and where they start and end.
Complete step-by-step answer:
Let us look at some of the basic definitions.
NUMBER: A number tells us how many times a unit is contained in a given quantity.
Types of number system:
1) Binary number system
2) Octal number system
3) Hexadecimal number system
4) Roman number system
5) Decimal number system
DECIMAL NUMBER SYSTEM: Numeric values are represented by using digits from 0 to 9.
Again numbers in the decimal system are classified as real numbers.
Real numbers are classified into rational numbers and irrational numbers.
Rational numbers are again classified into integer and non-integer rational numbers.
Again integers are classified into:
1) Positive integer
2) Negative integer
3) Whole number
4) Natural number
NATURAL NUMBERS: Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.
N = {1, 2, 3, …..}
Successor: Successor refers to the number directly after a given number, respectively.
To find the successor of a given number we need to add one to the given number.
Let us assume that the given number is a.
Hence, Successor of a will be a+1.
The successor function is denoted by S. So,
\[S\left( n \right)=n+1\]
As we know that natural numbers start from 1 and there is no certain end to that series.
N = {1, 2, 3, …..}
S for natural numbers will be:
\[\begin{align}
& \Rightarrow S=\left\{ 1+1,2+1,3+1, ….. \right\} \\
& \therefore S=\left\{ 2,3,4, ….. \right\} \\
\end{align}\]
Hence, as there is no specific end to natural numbers we can say that every natural number has a successor.
Note: The successor function is one of the basic components used to build a primitive recursive function.
Let us consider an example to find the successor:
Successor of 4 is 5 where 4 is the predecessor of 5.
Predecessor refers to the number directly before a given number. When we consider natural numbers we can say that not all natural numbers have a predecessor.
\[P\left( n \right)=n-1\]
If we calculate the predecessor of 1 we get 0. But, 0 is not a natural number.
So, 1 has no predecessor in natural numbers but all natural numbers have successors.
Complete step-by-step answer:
Let us look at some of the basic definitions.
NUMBER: A number tells us how many times a unit is contained in a given quantity.
Types of number system:
1) Binary number system
2) Octal number system
3) Hexadecimal number system
4) Roman number system
5) Decimal number system
DECIMAL NUMBER SYSTEM: Numeric values are represented by using digits from 0 to 9.
Again numbers in the decimal system are classified as real numbers.
Real numbers are classified into rational numbers and irrational numbers.
Rational numbers are again classified into integer and non-integer rational numbers.
Again integers are classified into:
1) Positive integer
2) Negative integer
3) Whole number
4) Natural number
NATURAL NUMBERS: Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.
N = {1, 2, 3, …..}
Successor: Successor refers to the number directly after a given number, respectively.
To find the successor of a given number we need to add one to the given number.
Let us assume that the given number is a.
Hence, Successor of a will be a+1.
The successor function is denoted by S. So,
\[S\left( n \right)=n+1\]
As we know that natural numbers start from 1 and there is no certain end to that series.
N = {1, 2, 3, …..}
S for natural numbers will be:
\[\begin{align}
& \Rightarrow S=\left\{ 1+1,2+1,3+1, ….. \right\} \\
& \therefore S=\left\{ 2,3,4, ….. \right\} \\
\end{align}\]
Hence, as there is no specific end to natural numbers we can say that every natural number has a successor.
Note: The successor function is one of the basic components used to build a primitive recursive function.
Let us consider an example to find the successor:
Successor of 4 is 5 where 4 is the predecessor of 5.
Predecessor refers to the number directly before a given number. When we consider natural numbers we can say that not all natural numbers have a predecessor.
\[P\left( n \right)=n-1\]
If we calculate the predecessor of 1 we get 0. But, 0 is not a natural number.
So, 1 has no predecessor in natural numbers but all natural numbers have successors.
Last updated date: 28th Sep 2023
•
Total views: 363.9k
•
Views today: 9.63k
Recently Updated Pages
What do you mean by public facilities

Please Write an Essay on Disaster Management

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is meant by shramdaan AVoluntary contribution class 11 social science CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

An alternating current can be produced by A a transformer class 12 physics CBSE

What is the value of 01+23+45+67++1617+1819+20 class 11 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
