(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.
(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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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