- Last time: the rationals are also countable, since they can be put into one-to-one correspondence with the natural numbers (this follows from the infinite number of infinite buses fitting into the Hotel Cardinality).
- Today:
- Reminder: a visit from Ed is coming up. Please think of questions
that you have of our author. I'd like his visit to be a highly
interactive one.
- Project ideas so far
- Homework Assignment #2 due today.
- Last time, Josh was getting onto 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:
- Next time: The Power Set, and
Russell's Paradox
Links:
Website maintained by Andy Long.
Comments appreciated.