Christy Case

Section 3:1/Due November 21, 2006

5. Bunch of Balls.  Your first job every morning at tennis camp is to get the ball machine ready for action. You open up some new cans of tennis balls and empty them into a large hopper. Is there a one-to-one correspondence between the balls and the can?

8. Don’t count on it. The following are two collections of the symbols @ and ©:

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @

Are there more @’s than ©’s? Describe how you can quickly answer the question without actually counting, and explain the connection with the notion of a one-to-one correspondence.

9. Here’s looking @ ®. The following collections contain the symbols @ and ®:

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @

® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ®

Are there more @’s than ®’s? Describe how you can quickly answer the question without actually counting, and explain the connection with the notion of a one-to-one correspondence.

10. Enough underwear. When Deb packs for a trip, she doesn’t count the number of days she will be away and then count out that many pairs of underwear. Instead, she places underwear into her suitcase, one at a time, and says the name of each day she will be away: “Monday” (and places one in), “Tuesday” (and places another in), “Wednesday,” etc. Using this method, does Deb know the number of underwear she placed in her bag? Does she have enough underwear for her trip? Discuss the connection this true story has with the notion of a one-to-one correspondence.

11. 791ZWV. Suppose a stranger tells you that the license plate number on his car is 791ZWV. If you had a listing of all automobiles in the United States together with their license plate numbers, would you be able to precisely identify the stranger’s vehicle? If so, explain why. If not, explain why, and identify what additional information you would require to identify it exactly. Discuss the connection between this situation and the notion of a one-to-one correspondence.

12. 245-2345. Suppose a stranger tells you that her telephone number is 245-2345. Would you be able to dial her number and be certain that you reach her? If so, explain why. If not, explain why, and identify what additional information you would require to be certain to reach her home. Discuss the connection between this situation and the notion of a one-to-one correspondence.

13. Social security (H). Is there a one-to-one correspondence between U.S. residents and their social security numbers? Explain why or why not.

16. Hair counts. Do there exist two nonbald people on Earth such that there is a one-to-one correspondence between the collection of hairs on one person’s body and the collection of hairs on the other person’s body? Feel free to use facts from previous chapters, but explain how they provide an answer to the one-to-one correspondence question.