Infinity, take 2:

1. Suppose the hotel was full, and a bus full of infinitely many people drove up.
A. What would you announce on the loudspeaker?
B. What rooms would the first 3 people on the bus be staying in?

2. Suppose the hotel was full, and 3 busses full of infinitely many people drove up
A. What would you announce on the loudspeaker?
B. For each of these people, tell what room you would put each in:

bus 1 person 1	bus 1 person 2
bus 2 personn 1	bus 2 person 2
bus 3 person 1	bus 3 person 2

C. Explain your pattern in assigning rooms to people

3. Suppose the hotel was empty, and infinitely many busses, each full of infinitely many people showed up. In what order would you assign rooms to people on the bus?

4. Show how we know that the set of rational numbers is the same size as the set of counting numbers (i.e. Show a 1-1 correspondence between the set of rational numbers, and the set of counting numbers).

5. Consider this infinite set of points.  (for each point the x-coordinate is an even number, and the y-coordinate is an odd number). Suppose that each of these points represents a person, who is going to check into the hotel infinity.  Show how you will fit them all in.  Show enough detail that I understand the pattern.  As part of your explanation, you should at least show who ends up in the first 10 rooms.



Answers.