
The smallest natural number is
[a] 0
[b] 1
[c] 2
[d] None of these
Answer
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Hint: Recall the definition of natural number. List them and try finding which is the smallest natural number from the list. Finally claim that number is the smallest natural number.
Complete step-by-step answer:
Natural Number: Number 1,2,3,… are called natural numbers. They are also known as counting numbers as these numbers are used for counting.
As can be seen from the definition 1 is the smallest natural number.
Claim: 1 is the smallest natural number.
Proof: Suppose not
Let there exists another natural number such that and a is a natural number.
Also since natural numbers have at least 1 as the difference between them
Hence we have
Since every natural number is >0, we have
Hence we have
Hence 1>1, which is a contradiction. Hence 1 is the smallest natural number.
Hence option [b] is correct.
Note: [1] The number 1 is called the greatest lower bound of natural numbers. A number m is said to be the greatest lower bound of a set A if and such that we have .
[2] Real numbers have greatest lower bound property,i.e. if a set A which is a subset of R has a lower bound, then A has greatest lower bound also. The natural numbers have a lower bound 0. Hence according to this property they have the greatest lower bound also which is true since 1 is the greatest lower bound of natural numbers.
Complete step-by-step answer:
Natural Number: Number 1,2,3,… are called natural numbers. They are also known as counting numbers as these numbers are used for counting.
As can be seen from the definition 1 is the smallest natural number.
Claim: 1 is the smallest natural number.
Proof: Suppose not
Let there exists another natural number
Also since natural numbers have at least 1 as the difference between them
Hence we have
Since every natural number is >0, we have
Hence we have
Hence 1>1, which is a contradiction. Hence 1 is the smallest natural number.
Hence option [b] is correct.
Note: [1] The number 1 is called the greatest lower bound of natural numbers. A number m is said to be the greatest lower bound of a set A if
[2] Real numbers have greatest lower bound property,i.e. if a set A which is a subset of R has a lower bound, then A has greatest lower bound also. The natural numbers have a lower bound 0. Hence according to this property they have the greatest lower bound also which is true since 1 is the greatest lower bound of natural numbers.
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