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Unformatted text preview: Honors Introduction to Analysis I Homework I Solution February 2, 2009 Problem 1 1. There is a positive integer that either doesn’t have a prime factorization, or it has several prime factorizations. 2. There are other even primes except 2. 3. Multiplication is not associative. 4. There are two points in the plane such that no line contains both of them. 5. There is a triangle for which the altitudes either don’t intersect in any point or intersect in several points. 6. There exist a line and a point not on it such that either there is no line parallel to that line and going through that point or there are several distinct lines going through that point, which are parallel to that line. 7. There is a partitioning of the integers into a finite number of disjoint subsets such that none of its subsets contains arbitrarly lonng arithmetic progressions. 8. There are either less letters than mailboxes or at least one mailbox has more than one letter (equivalently: if there are more letters than mailboxes, all mailboxes have at most one letter) Problem 2 1. There is a point which is the midpoint for all line segments.1....
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 Fall '08
 PROTSAK
 Natural number, Cardinal number, countable subset

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