Lecture 3, September 12.

Material covered: Rudin Pages 15-17, 24-26

  1. Schwarz inequality.
  2. Triangle inequality.
  3. Maps, surjectivity, injectivity, bijectivity.
  4. Finite sets, countable sets, uncountable sets, at-most-countable sets, infinite sets.
  5. Countability of the integers.
  6. A countable union of countable sets is countable.
  7. Cartesian product of two countable sets is countable.
  8. Countability of the rationals.
  9. The noncountability of the set of sequences with values in {0,1}.
  10. Metric spaces, definition and examples - Euclidean metric, discrete metric and supremum metric.