Natural numbers N 1,2,3,…These are closed under Addition.
Exercise 1.1 Is Z countable? Solution
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
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,