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Give an example of a function f:N->Z that is surjective but not injective
Solution
let f(x) = floor(x * sinx)
since sin x can be negative , it will cover both the positive and negative integers
and x * sin x is periodic , so it cannot be injective
hence f(x) is surjective but not injective

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Give an example of a function fN-Z that is surjective but not inje.pdf

  • 1. Give an example of a function f:N->Z that is surjective but not injective Solution let f(x) = floor(x * sinx) since sin x can be negative , it will cover both the positive and negative integers and x * sin x is periodic , so it cannot be injective hence f(x) is surjective but not injective