Class 6: More Infinity

This last week before break, we went more in-depth into infinity.

  1. We did a coloring exercise and learned that we can add up infinitely many numbers and still get only 1. You can find the exercise here.
  2. We talked about why 1/3=0.333333… and why 0.9999999…=1 (even though that seems nuts). We also watched this Vi Hart video about why: https://www.youtube.com/watch?v=TINfzxSnnIE.
  3. We reviewed ideas about one-to-one correspondence as a way of deciding if one set is bigger than another, reminded ourselves that there the same number of even numbers as all the counting numbers. Then we talked about whether if we had infinitely many piles of m&ms, each of which had an infinite number of m&ms, would that be a larger infinity that the counting numbers (the answer is no). 
  4. To find a new infinity we need to not focus on counting numbers, we need other types of numbers — you can find a summary of the different types we discussed here: http://www.purplemath.com/modules/numtypes.htm. Remember that last week we watched Vi Hart explain a little about irrational numbers and why pythagoras was really wierd here: https://www.youtube.com/watch?v=X1E7I7_r3Cw.
  5. Next class, we will be showing that there are more real numbers between 0 and 1 than there are counting numbers. Do do that we first explored a game I call “virtual dodgeball.”
  6. You also have a new project assignment. See all of the details here.
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