(a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b) Prove that there exists a function g : R → R so that g is onto but g is not one-to-one.

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(a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto.
(b) Prove that there exists a function g : R → R so that g is onto but g is not one-to-one.
Transcribed Image Text:(a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b) Prove that there exists a function g : R → R so that g is onto but g is not one-to-one.
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