Homework_set_2_typeset - good deal harder. In my copy of...

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Math 413, Fall semester, 2007 Bigtimes Homework set 2, handed out August 30. due September 6 Read all of Chapter 2; sections 2.4.3 and 2.4.4 may be viewed as optional. In the text, do exercises 1, 3, 4, 5, 7, 9 of section 2.2.4. All are easy, 5 is the trickiest, and still not too bad; remember that all you know about a real number is that it is an equivalence class of Cauchy sequences of rationals. In the text, do exercises 1, 3, 5, 6, 8 of section 2.3.3. These, especially 5 and 6, are a
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Unformatted text preview: good deal harder. In my copy of the text, there is a misprint in exercise 5: the coecient k n +1 of the continued fraction should be k n-1 . Finally, just to make sure you read the sections on Dedekind cuts, in Sections 2.4.5, do exercises 1, 3, 4. This last is a famous conundrum; it should make you think a bit. The above should keep you busy....
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