File:Cantors Diagonal Method.pdf

Cantor’s diagonal method is elegant, powerful, and simple. It has been the source of fundamental and fruitful theorems as well as devastating, and ultimately, fruitful paradoxes. These proofs and paradoxes are almost always presented using an indirect argument. They can be presented directly. The direct approach, I believe, (1) is easier to understand, (2) unifies the proofs and paradoxes by exhibiting a single strategy, (3) shows Russell’s paradox to be the (obvious?) ultimate, set theoretic application of the method, and (4) is extendable to some of the semantic paradoxes.