Day 14 in Mat115

Today:

• Rationals, Irrationals and Reals....
  • Irrational Problems:
    • Find a rational number between 1001/1003 and 1002/1003

    • Find an irrational number between 1001/1003 and 1002/1003!

    • Can you find a rational number between two irrationals?

  • The real numbers are all the rationals and the irrationals together, usually represented on the "real number line". Did you get out your 3-D glasses, and have a look at the figure on p. 126? What does the figure show?

  • Why does every interval on the real line contain an infinite number of rational numbers?

  • Why does every interval on the real line contain an infinite number of irrational numbers?

  • Describe the argument given for the claim that there are more irrationals than rationals.

• Questions about homework?

Next time: Section 3.1: Beyond Numbers (ChrisB, Alisha)