Day 15: Heart of Mathematics

Last time: Real Numbers. We might want to spend a few minutes on the problems we didn't get to last time....
Today:
- Reminder:
  - Homework assignment #2: For Friday, fix assignment 1!
    Remember: Hand in your assignment 1 with assignment 2! I want to see improvement, of course!
  - Project Assignment 2 (due 10/4): let me know what your topic is, and some preliminary details about what your poster will cover.
- More Project ideas proposed:
  - The Mathematics of Poverty
  - Mathematics Across Cultures
- Infinity - so mysterious! (Are mathematicians trying to take all the fun out of it?! Of course not! We relish the mind-blowing mystery....)
  
  William Blake (from Auguries of Innocence):
  To see a World in a Grain of Sand
  And a Heaven in a Wild Flower,
  Hold Infinity in the palm of your hand
  And Eternity in an hour.
- We start with the idea of number (e.g. What does "2" mean?).
- What is a one-to-one correspondence, and how is it useful?
- Let's look at some problems:
  - I.1-3
  - II.1 (are the natural numbers as numerous as the natural numbers?)
Next time: Getting to infinity one thing at a time (via one-to-one correspondences)

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