Homework Assignment Twelve

You may collaborate on 9

  1. 9.1.4 [textbook editions 3,4,5,6]
  2. 9.1.12 [textbook editions 3,4,5,6]
  3. 9.2.4 [textbook editions 3,4,5,6]
  4. 9.2.10 [textbook editions 3,4,5,6]
  5. 9.3.4(b) [textbook editions 3,4,5,6]
  6. 9.3.14 [textbook editions 3,4,5,6]
  7. 9.4.2a,b [textbook editions 3,4,5,6]
  8. 9.4.10a [textbook editions 3,4,5,6]
  9. (extra credit) - below
Consider all unordered (distinct) pairs of positive integers. Call this set S. Now color the elements of S in any way imaginable using two colors, say red and blue. Prove that either there is an infinite subset of integers, all of whose two element subsets are red, or there is an infinite subset of integers all of whose two element subsets are blue.[Problem says: "there are an infinite number of people at a party; then either an infinite number of people are all mutually acquainted, or an infinite number of people are mutual strangers".]

Due: (Absolutely) Thursday December 4, in class

-- RobbieMoll - 03 May 2009

Topic revision: r6 - 2014-11-29 - RobbieMoll
 
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