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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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 Fall '07
 HOPCROFT

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