## Math in the Middle Institute Partnership

#### Title

#### Date of this Version

7-2006

#### Abstract

I have been assigned to explore the theorem stating that there is no largest (infinite) set as established and proven by Georg Cantor. To do this I need to start by defining what it means to say that a set is infinite. This can be quite difficult because the tendency might be to say that a set is infinite if it is not finite, and I don’t believe that grants us the clarity of definition we are looking for. When trying to understand the size of a given set, the number of objects (elements) in the set, we may not be able to count them as the total might be quite large. So we look to pair them evenly with objects of other sets or proper subsets of themselves: this is known as finding a one-to-one correspondence.

## Comments

In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. David Fowler, Advisor July 2006