# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### CANTOR #6: Attempts to Invalidate Cantor’s Work

(February 9, 2016)  Our last session.Sigh. TRANFINITE ALGEBRA When I had asked the students two weeks ago what topics they wanted to be sure to hit in this course, F had responded “something with more answers than questions, something definite.”  I came prepared with a list of “the sort of algebraic conclusions that only a special notation for the transfinite…

### CANTOR #5: Set Theory

(February 2, 2016)  My recap of our session is going to be hard to write about for 2 reasons:  (1)  I’m writing it almost a month later, and (2) we used a lot of jargon and symbols that parents may not understand.  But, I remember the big picture, and I’ll try to explain the math concepts and/or give you some…

### 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…

### 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…

### 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…