Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
MENU
Learning Math Home
Patterns, Functions, and Algebra
 
Session2 Part A Part B Part C Homework
 
Glossary
Algebra Site Map
Session 2 Materials:
Notes
Solutions
Video

Session 2:
Homework

Problem H1

Solution  

Divide the number 1 by the numbers 1 through 10 consecutively. What conjectures can you make about rational numbers when represented as decimals?


 

Problem H2

Solution  

If we think of division as a repeated subtraction, can you explain why it is impossible to divide by 0?


 

Problem H3

Solution  

In a hotel with an infinite number of rooms and a counting number assigned to each, there is a "No Vacancy" sign outside. A traveler comes in and asks for a room for the night. How does the staff accommodate this traveler?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think of the traveler as one more element to add to a countably infinite set. Is the new set also countably infinite?   Close Tip

 

Problem H4

Solution  

In a hotel with an infinite number of rooms and a counting number assigned to each, there is a "No Vacancy" sign outside. An infinite marching band -- one where each member has a unique number on his or her uniform -- enters and asks for a room for the night for each musician. How does the hotel staff accommodate everyone?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think of the band and the rooms as two infinite sets to be added together. What kind of set do you get? How can you put this new set into one-to-one correspondence with the counting numbers?   Close Tip

 

Problem H5

Solution  

There's an infinite chain of infinite hotels, each with a unique address on the street. All of them are full. But one night, very suddenly, all but one of them go out of business! How does the one remaining hotel accommodate all the stranded guests?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think of this as adding together an infinite number of infinite sets. This will be similar to putting rational numbers into one-to-one correspondence with the counting numbers.   Close Tip

Suggested Readings:

Read History and Transfinite Numbers: Counting Infinite Sets.

Download PDF File:
History and Transfinite Numbers: Counting Infinite Sets.


Next > Session 3: Place Value

Learning Math Home | Number Home | Register | Glossary | Map | ©

Session 2: Index | Notes | Solutions | Video

Home | Catalog | About Us | Search | Contact Us | Site Map

  • Follow The Annenberg Learner on Facebook

© Annenberg Foundation 2013. All rights reserved. Privacy Policy