Give example of a function f: N-> N which is:

(a) injective but not surjective.

(b) surjective but not injective.

(c) bijective but not identity function.

Question

Felix

Mathematics

13 December, 10:17

Give example of a function f: N-> N which is:

(a) injective but not surjective.

(b) surjective but not injective.

(c) bijective but not identity function.

+1

Answers (1)

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Bart · Answer 1

An injective function is not a function that is surjective. This means that you want a function that has a unique output for each input, that doesn't cover the natural numbers.

In formal terms a function [Math Processing Error] is injective if [Math Processing Error] implies [Math Processing Error].

We also know that it's not surjective because no value maps to [Math Processing Error] (or any odd number) since if [Math Processing Error], then [Math Processing Error]. However, since [Math Processing Error], the function isn't surjective.

Answer is B.

Give example of a function f: N-> N which is:(a) injective but not surjective.(b) surjective but not injective.(c) bijective but not identity function.

Give example of a function f: N-> N which is:

(a) injective but not surjective.

(b) surjective but not injective.

(c) bijective but not identity function.