Day 11: Heart of Mathematics

• Last time: Comparing the infinite
  • Here's a neat idea of a way to fill up the hotel when an infinite number of natural number-sized buses show up (actually, we wouldn't have to fill the hotel - there would still be an infinite number of rooms left after we were done!).
    • Associate each bus with a prime number, then
    • put individuals into prime power rooms.
    This relies on the unique prime decomposition of each natural number.

• Today: 3.3: The Missing Member (some infinities are bigger than others!)
  • Remember: test 1 on Monday

  • Return homework 2.4

  • Before we begin: .999999.... = 1.000000....

  • The proof: "Dodge Ball" revisited

    "From the paradise created for us by Cantor, no one will drive us out."

    David Hilbert.

  • Let's look at the problems, pp. 168-:
    • 13
    • 14
    • 19

• Next time: Exam 1

Links:

• George Cantor, driven to distraction (or at least depression) by infinity!
• David Hilbert