University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Number Theory"
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.