University of Nevada Las Vegas
Howard R. Hughes College of Engineering
Department of Computer Science
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CSC 456/656 Assignment 7

Due date: Tuesday, March 15, 2016, 4:00 PM.

All assignments must be handwritten (not typed or printed from a computer file) in your own handwriting, on 8.5 by 11 inch paper, or on A4 paper. Write your name on each sheet, and do not fold the pages or crimp the corners. (You may use a paper clip or a staple.)
Turn the pages in to me or to the graduate assistant on or before the due date.

  1. Prove the square root of 3 is irrational. (By contradiction.)
  2. Prove that the sum of the first n squares of positive integers is (2n3+3n2+n)/6. (By induction.)
  3. Prove that every language is enumerable. (You may assume that the alphabet is the binary alphabet.)
  4. Prove that the set of real numbers is not enumerable. (By diagonalization.)

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