At the beginning of this year I bought a copy of Richard Evan Schwartz’s Gallery of the Infinite:
We ended up doing a fun project using the book:
Yesterday I saw the book on our shelf and asked the boys to find something in it that they thought was interesting. The section on bijections caught the eye of my younger son, and we used that section for a project today.
First we talked about the basic idea of bijections and how you could use bijections to tell if two sets were the same size:
Next we talked about a bijection that is pretty challenging for kids to find -> a bijection between the positive integers and the set of all integers:
Finally, we talked through Cantor’s “diagonal argument” which shows that there is no bijection between the integers and the real numbers (and, thus, that the “infinity” of real numbers is somehow larger than the “infinity” of integers!):
Tomorrow we’ll talk through the section of the book that my older son thought was interesting -> the Cantor set.