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Mathematics, 10.02.2020 23:59 johnandashley5p65r4a
Exercise 1.5.1. Finish the following proof for Theorem 1.5.7. Assume B is a countable set. Thus, there exists f : N β B, which is 1β1 and onto. Let A β B be an infinite subset of B. We must show that A is countable. Let n1 = min{n β N : f(n) β A}. As a start to a definition of g : N β A, set g(1) = f(n1). Show how to inductively continue this process to produce a 1β1 function g from N onto A.
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Exercise 1.5.1. Finish the following proof for Theorem 1.5.7. Assume B is a countable set. Thus, the...
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