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302 HW 8 - He can just tell each guest that if the guest is...

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M302 HOMEWORK #8 Dr. Schurle Assignment: page 156, #4, 8, 11, 16, 30, 32, 38 Grade the following for 2 points each, then give all or part of the remaining two points depending on how much work they've done on the other problems. #4. The set of all even natural numbers and the set of all reciprocals of the natural numbers are both infinite sets. The set of all natural numbers less than 10 and the set of solutions to the equation x 2 4 = 0 are both finite sets. #8. One way to show this is by these “matching” lists: 1 2 3 4 5 6 7 ... 5 15 25 35 45 55 65 ... OR, from this matching, we can get a formula for the matching: the natural number n matches with 10 n – 5. #16. Yes, the manager can provide the traveler with a private room.
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Unformatted text preview: He can just tell each guest that if the guest is in room N, then the guest must move to room N+1. That frees up Room 1 for the traveler. #30. Yes. Here is one way to see a one-to-one matching between the natural numbers and all the bars in all the packages: Natural numbers: 1 2 3 4 5 6 ... Packages 1 2 3 ... Candy bars bar bar bar bar bar bar ... More “mathematically,” we match one bar in Package # n with the natural number 2 n and the other bar in Package # n with the natural number 2 n-1. Either of these descriptions are good and enough – there may even be other descriptions of this matching....
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