

Natural numbers N 1,2,3,…These are closed under Addition. Exercise 1.1 Is Z countable? Solution Multiplication Exercises: 1.2 Is Q countable? (see picture for hint) Solution 1.3 Prove or disprove: a countable set of countable sets is countable. Solution Decimal form of numbers Exercises: 1.4 Are there other decimal numbers? Solution 1.5 Are all decimal numbers countable? (see picture for hint) Solution A number which differs from each number k in the kth decimal digit # cannot be on the list of numbers! Algebraic numbers: these are solutions to polynomial equations, with integer coefficients. Exercise 1.6 Are algebraic numbers countable? Solution Real Numbers R = all decimal numbers, Other numbers? 