Day 17: Heart of Mathematics

• Last time: cardinality measures the size of infinite sets. Everyone's welcome at Hotel Cardinality! These infinite sets contain no "last" member.

• Today:
  • The first project assignment is due: I need a one-page statement about your project intentions.

  • Reminder: Homework Assignment 2 (due 10/6)

  • Project idea: Zeno's Paradoxes

  • Rational numbers are countable? One more visit to Hotel Cardinality....

  • Which ping pong ball is left in the barrel? (the time steps are related to Zeno's paradoxes....)

  • A related problem: Thompson's Lamp

  • Let's look at the problems:
    • II.7
    • III.1

• Next time: Infinities!

Links:

• A colorful version of the Hotel Infinity story (here's a local copy)
• Thompson's lamp
• An Introduction to Infinity (You can't get there from here). local copy
• What is a number? local copy
• More on Zeno local copy
• The guy who introduced me to Zeno, on the paradoxes (a little dry, however!)
• Zeno's Paradox of the Tortoise and Achilles local copy