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CS202: Discrete Structures

3.2: Numbers: Direct Proofs and Counterexamples
- Logic has application to other parts of mathematics, not just to reasoning about the world. The following subunits apply logic to statements about numbers.
- 3.2.1: Rational Numbers
  - University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory" URL
    Read Section 1: "Basic Facts about Numbers," example 4 on page NT-5. This example proves an important property of rational numbers using a constructive proof technique. This reading also applies to the topic in subunit 3.2.3 of this course.
- 3.2.2: Irrational Numbers
  - University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory" URL
    Read Section 1: "Basic Facts about Numbers," example 5 on pages NT-5 and NT-6 and example 6 on pages NT-7 - NT-9. Example 5 proves a property of real numbers using counterexamples. Example 6 applies to integer, rational, and real numbers.
- 3.2.3: Proving Properties of Rational Numbers
  - Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Notes for Recitation 2" URL
    Read the recitation on pages 1 - 5. These give more examples of proof techniques for numbers.