Day 19: Heart of Mathematics

Last time: the real numbers are not countable, since they cannot be put into one-to-one correspondence with the natural numbers.
Today:
- Reminder:
  On Monday, Oct. 13th, Ed Burger will be visiting our classroom, and leading discussion.
  Your job: Please come prepared with a question that you would like to ask Ed. It could concern your poster, some topic we've considered together in class, or anything else, as long as it is not frivolous. It should demonstrate that you carefully thought about your question ahead of time, and didn't just make it up on the spot....
- An infinity of infinities:
  - Question 5 (to add to the 4 on pages 174-175):
    Are there only a countable number of different sized infinities?
  - Sets and subsets (Look at problem I.1)
  - Power sets
  - Cantor's proof that the power set has larger size (cardinality) than the set itself (recycling his proof that the reals are bigger than the naturals!).
  - Let's look at the problems:
    - I.1
    - I.8
Next time: The geometry of infinity

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