Theory of Computing Homework 1 CS 3810, Fall 2009 Due Friday, September 4 General guidelines: You may work with other people, as long as you write up your solution in your own words and understand everything you turn in. Make sure to justify your answers—they should be clear and concise, with no irrelevant information. 1. Write a short essay about diagonalization that would explain to a high school senior the concepts of countably infinite, non countably infinite, and diagonalization. It should talk about how to compare the cardinality of two sets and it should give contain a convincing argument that there exists a non countably infinite set. 2. Countability a) Prove that the set of all finite length strings over a finite alphabet is countably infinite. b)
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