Exploring and developing connections between mathematics and art

Week 2: What is Infinity? Plus Zeno’s Paradoxes

This week, we talked about the mathematical memories that everyone came up with — thanks to all for the powerful discussion! Then we moved on to

One-to-one correspondence. This is a fancy name for something more basic than counting — matching up two collections to decide whether or not they are the same size. See this video: http://ed.ted.com/lessons/how-big-is-infinity, which also introduces lots of other ideas about infinity.

Sets, subsets, and proper subsets. A “set” is a collection of things. If we take a set, and we make a group of just some of the things, that’s a “subset.” If we make sure that group we make doesn’t contain everything in the original set, then that’s a “proper subset.” So, for instance, in the set that contains all of the letters of the alphabet, one example of a proper subset is all of the consonants. Another would be the set {a, b, c, d}. There are lots of proper subsets of the alphabet!

Mathematicians say that a set is “infinite” if we can put it in one-to-one correspondence with a proper subset of itself. Whoa. More talk about this in class. We also did some practice with these ideas in class.