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hw30 - Let X and Y be(nonempty sets and let f X → Y be a...

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Intro to Abstract Math Homework 30 Fall 2009 Due December 7 Exercise 87. Let a Q , a 6 = 0. Prove that the function f : Q Q given by f ( x ) = ax is an isomorphism. Conversely, show that if g : Q Q is an isomorphism then g ( x ) = ax for some nonzero a Q . Exercise 88.
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Unformatted text preview: Let X and Y be (nonempty) sets and let f : X → Y be a bijection. Prove that X is countable if and only if Y is countable. [ Suggestion: Consider the finite and infinite cases separately.]...
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