Functions - Basic

Algebra Level 3

Define the mapping σ : N → N \sigma : \mathbb{N} \rightarrow \mathbb{N} such that σ ( n ) \sigma(n) is the successor of n n [ For example, σ ( 3 ) = 4 , σ ( 4 ) = 5 \sigma(3)=4, \sigma(4)=5 , etc.. ]. Then, this mapping is :-

Surjective and Non-Injective function Injective and Non-Surjective function Bijective function Not a function

Venkata Karthik Bandaru by Venkata Karthik Bandaru , 20, India

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1 solution

After seeing the diagram of the mapping, we see that the mapping is defined for all elements of the domain uniquely, and hence the mapping is a function. But in the range, the element 1 1 is left unmapped. Hence, the function is injective and non-surjective.

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