Sets and Mathematical Proofs: A Primer

Sets and Mathematical Proofs: A Primer

Pre-preamble: Is it worth your time to read this primer?

If you have taken rigorous mathematics courses in university, you likely know everything here already. Please briefly skim the primer to confirm.

If you have not taken any significant amount of mathematics at university yet, this primer is for you.

A note on this web version. Wherever a proposition or definition is cited, you can click the citation to see it. To go to the place in the primer where it first appears, press “Go to”.

The web version is the recommended one, but a PDF version is available if you would rather print it or read it offline.

Contents

  1. 1Introduction
  2. 2What is a set?
  3. 3The axiom of extensionality
  4. 4Sets within sets
  5. 5Roster notation
  6. 6Inclusion criterion notation
  7. 7What sets are there?
  8. 8Subsets
  9. 9More about subsets
  10. 10The empty set
  11. 11Equivalent inclusion criteria
  12. 12Intersections
  13. 13Unions
  14. 14Interactions between Unions and Intersections
  15. 15Relative complements
  16. 16Complements
  17. 17Disjointness
  18. 18Collections of sets
  19. 19Partitions
  20. 20Summary of results
  21. 21List of Exercises