Day 18: Heart of Mathematics

• Last time: Problems

• Today: 3.3: The Missing Member (Danny, Jeff)
  • Project ideas so far

  • 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.

  • 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:
    • I.4, 6, 8, 9
    • II.1, 2, 4.

• Next time: 3.4: Travels Toward the Stratosphere of Infinities (Dane, Christy)

Links:

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