The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

CANTOR #4: Diagonal Proof

(January 26, 2016) “COUNTING” THE RATIONALS We began where we left off last week:  how can one list the set of rational (fractions and integers) numbers in a one-to-one correspondence with the naturals (counting) numbers? I gave the students some time to work on it, and everyone came up with a way to do it. (See photos for variations.)1  Everyone…

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CANTOR #3: Math is Freedom

(January 19, 2016)  “I realized as soon as we left class last week that there was a big mistake in our Venn Diagram of number types,” I said to start our session today. “Huge?” asked someone. “Enormous,” I teased.   VENN DIAGRAM REPAIR I felt like we then played “Twenty Questions” as the students narrowed and narrowed their conjectures about…

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CANTOR #2: Realen and Reellen Numbers

(January 12, 2016)  We had a small group of 3 teens today, so to start the session on an energetic note, I shamelessly presented some controversial material. I showed the students E.T. Bells’ 1937 book Men of Mathematics, a book many consider an accessible classic of math history.  I’ve relied on this book for various math circle discussions over the…

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CANTOR #1: Let’s Say I’m a Millipede

(January 5, 2016)  “Are there more books or bookcases in this room?” This question thus began our first math circle of the new year. “Do you mean bookshelves or bookcases, not that it would make a difference?” asked W.  Everyone agreed immediately that there are more books.   ONE TO ONE CORRESPONDENCE “How could you tell without counting?” I asked….

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