Cantor Archives - Harmony Learning Community

CANTOR #6: Attempts to Invalidate Cantor’s Work

Posted by Rodi Steinig

· Thursday, March 17th, 2016

(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

Posted by Rodi Steinig

· Friday, February 26th, 2016

(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

Posted by Rodi Steinig

· Monday, February 1st, 2016

(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

Posted by Rodi Steinig

· Wednesday, January 20th, 2016

(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

Posted by Rodi Steinig

· Sunday, January 17th, 2016

(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…

CANTOR #1: Let’s Say I’m a Millipede

Posted by Rodi Steinig

· Thursday, January 7th, 2016

(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….

INFINITY 3: Refining our Definition of Infinity

Posted by Rodi Steinig

· Tuesday, December 2nd, 2014

(November 25, 2014) Rather than my conventional in-depth play-by-play, this is a quick report on the highlights of our last session. With the Thanksgiving holiday, 2 kids were absent, so our group size was 5. MATH RED LIGHT GREEN LIGHT, CONT’D This week, we switched to “snails,” vs. live humans, as the playing pieces in our game. Everyone adopted…