) Suppose that S is an infinite set and f : N → S is onto S. Explain how to define a function g : N → S that is both one-to-one and onto S. Suggestion: Let g(1) = f(1) and having defined g(1),.., g(k), explain how to define g(k +1).

) Suppose that S is an infinite set and f : N → S is onto S. Explain how to define a function g : N → S that is both one-to-one and onto S. Suggestion: Let g(1) = f(1) and having defined g(1),.., g(k), explain how to define g(k +1).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 12E: Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.

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Question

) Suppose that S is an infinite set and f : N → S is onto S. Explain how
to define a function g : N → S that is both one-to-one and onto S. Suggestion: Let
g(1) = f(1) and having defined g(1), ..., g(k), explain how to define g(k + 1).

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