Lecture 26

We covered sections 20.6-20.9. Specifically, we used diagonalization to show that the power set of the integers, as well as the reals, are uncountable. We then looked at some sample countable and uncountable sets. And then at applications of uncountability to computability and tiling/Chemistry.

Pictures of tilings:

• tilings in real life
• regular tilings
• Wang tiles
• aperiodic tiling pictures
• Penrose tiling showing 5-fold symmetry
• quasicrystals

Announcements

• ICES in discussion this week, lecture next Tuesday.
• Final exam conflicts must be reported to instructors by next Wednesday.
• No homework due next week.
• Reminder: the second honors homework is due next Monday (May 5th).
• Discussion attendance numbers should appear on Moodle over the weekend. Check that yours is correct. There were 13 discussions but we're dropping one, so the maximum score is 12.
• Final exam
  • Check for final exam conflicts NOW.
  • Review materials are mostly up.
  • Office hours next week as normal.
  • Watch for information on room assigments for the final.