Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Prove each of the following statements:
(a) ∃f : N → N for which f is 1-1 and onto.
(b) ∃f : N → N for which f is 1-1 but not onto. (c) ∃f : N → N for which f is onto but not 1-1.
(d) ∃f : N → N for which f is neither 1-1 nor onto.
[Note: feel free to draw bubble-arrow pictures here, but make sure you explain what’s
going on very carefully.]

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Step 1: Definition of 1-1 and onto function
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Step 2: Example of subparts (a) &(b)
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Step 3: Example of subparts (c) &(d)
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