Logic1102 - HW #6 (due 11/4) 1. Problem 13.12 (prove by a...

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Unformatted text preview: HW #6 (due 11/4) 1. Problem 13.12 (prove by a tableau) 2. Exercise 13.7 (p.129, in the first for- mula “Kx” should be “~Kx”) 3. Show that the set of all rational num- bers (of the form a/b where a and b are integers – could be negative – and b≠0) is denumerable. Read Ch.15 and the first few pages of Ch.16 (will continue for the next week). Denumerable sets N: set of all natural numbers (all even and odd #s) Q: set of all rational numbers (all frac- tions) The set of all finite subsets of the above (14.16) Non-denumerable sets Set of all subsets of N R: Set of real numbers (the continuum ) Illustration: a book with denumerably many (infinite) pages – Page 1, Page 2, …, Page n, … . On each page is written down a description of a set of positive in- tegers. (ex. p.151) Is it possible to list (enumerate) every set – both finite and infinite – of positive integers in this book? No. No matter how hard you try, there is a set of positive integers that is not listed in the book. (proof by contradiction) Suppose that every set of positive integers is listed in the book. Let S1 be the set described on Page 1, S2 the set on Page 2, …, Sn the set on Page n, … ....
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This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

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Logic1102 - HW #6 (due 11/4) 1. Problem 13.12 (prove by a...

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