Homework_set_3_typeset - solution but perhaps you could...

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Math 413, Fall semester, 2007 Bigtimes Homework set 3, handed out September 6 due September 13 Read through Section 3.2 of Chapter 3. In the text, do exercises 1, 2, 4, 5, 7, 9 of section 3.1.3. I think that all of these are easy. Problem 1. What do you think of sup n N sin 10 n . I am of ourse measuring angles in radians. I don’t expect people to actually solve this (I don’t think anyone knows the
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Unformatted text preview: solution), but perhaps you could guess what the result ought to be, and see that for this to occur, there must be infinitely 9’s or 0’s in the decimal expansion of 1 / 2 π . In the text, do exercises 1, 5, 6, 9, 11 of section 3.2.3. These Problem 2. Show that the numbers of the form n + m √ 2 is dense in R . This is pretty tricky!...
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