homework9 - LOGIC AND PROOF HOMEWORK 9 1. Use the...

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Unformatted text preview: LOGIC AND PROOF HOMEWORK 9 1. Use the pigeonhole principle to prove that if there are six people at a party, then there is either a set of three mutual friends or a set of three mutual strangers. [Hint: Start with a hexagon containing the six people. Consider one person, and use different colored lines to denote friends and strangers.] 2. Prove that the set of positive integers is equivalent to the set of integers. 3. Prove that the set P = {X ( +) | X is finite} is denumerable. 4. 5.2.10 5. 5.3.10 (parts a and b) 6. Use the Cantor‐Schroder‐Bernstein Theorem to carefully explain why x . [Note: This proves that the unit square has the same cardinality as the length of one of its sides. After he proved this Cantor famously wrote to Dedekind that "I see it, but I don't believe it!"] 7. Explain in simple terms what the Cantor Set is, providing a diagram. Prove that it is uncountable. 8. What’s yellow and equivalent to the axiom of choice? Give the answer to the joke, and provide the real answer (ignoring the color), along with the statement of the result. ...
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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