10-07-quiz-2 - x 2 0 for all real numbers x ? Proof....

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Sets and Logic — Fall 2011 Name: Quiz #2 1 Prove that for every real number x , if x > 2 then there is a real number y such that y + 1 / y = x . 2 Suppose that F and G are families of sets, and every element of F is a subset of every element of G . Prove that u F ⊂ i G . 3 What’s wrong with the following proof of the fact that
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Unformatted text preview: x 2 0 for all real numbers x ? Proof. Suppose not. Then for every real number x , x 2 < 0. In particular, plugging in x = 3, we would get 9 < 0, which is clearly false. This contradiction shows that for every real number x , x 2 0....
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