Abstract: One of the first "things mathematical" that we learn to do is to count our "stuff" (toys, money, cars, whatever...). This task is pretty easy, since (most of us) only have a finite number of things to count. But how does one go about counting a set of objects that has infinitely many elements (and is this possible)?

Here are some warm-up questions for the talk:

1) Which is "bigger", the set of of integers, the set of rational numbers (fractions that can be created from quotients of two integers), or the set of real numbers?

2) Suppose that I have infinitely many ping-pong balls, one numbered 1, one numbered 2, one numbered 3, and so on. Suppose that I have a large bag and I play the following game: At one minute before midnight, I put balls numbered 1 through 10 in the bag and then immediately remove ball 1. At 1/2 a minute before midnight, I put balls 11-20 in the bag and remove ball number 2. At 1/3 a minute before midnight, I put balls 21-30 in the bag and remove ball three. If I continue this process, how many balls are left in the bag at the stroke of midnight?

The answers to these (and other) questions will be explored. This talk will be very elementary and requires only high school background. I am willing to bet that before the hour is up, I can surprise you on more than one occasion!