Counting for Advanced Mathematicians
Brian Simanek, Vanderbilt University
Location: Stevenson 1206
Our mathematics education parallels the history of mathematics in that it all began with counting. At a very young age, we understood the idea of quantity and - more importantly - how to compare quantities. Then, somewhere along the way we vaguely became aware of this mysterious idea called infinity that somehow answered the question we all posed to our first grade teachers: "What is the largest number?" The main point of this talk will be to demonstrate that infinity does not really answer this question because there are different sizes of infinity! As strange as this may seem, we will try to understand how this can be the case and mention some different ways that mathematicians describe the size of a set when counting is not sufficient.