Math Class
The Infinite in Mathematics
Mathematics routinely deals with infinitely large sets of objects. At first, it may seem rather implausible that we could say much of anything very definite about such fundamentally indefinite collections. How, for example, can we know something about all integers, when nearly all integers are much larger than we could possibly comprehend? In this short course, we’ll investigate several methods for exploring the infinite, as well as their fascinating and sometimes counterintuitive results.

Introduction, Infinity of Primes and the Sparsity of Primes, Some “Big” Numbers

Proofs about the Natural Numbers, Mathematical Induction

Fundamental Concepts in the Mathematical Analysis of Infinity

The Denumerability of the Rationals

The NonDenumerability of the Reals