As a counterpoint to Kids and Infinity, here’s to Grown-ups and Infinity.
Jan of Think Again raised Galileo’s Paradox on his blog: The question of whether there are more fewer even natural numbers than natural numbers overall. This has led to some good discussion of the various countably infinite sets, which are, counter-intuitively, considered to be equinumerous or of the same cardinality.
Darmok provided a great link to this article: Infinity: You Can’t Get There From Here which provides a well-written and understandable discussion of infinite cardinalities. I liked it enough to post a link to it here. Don’t be afraid to click on the link to the proof of Cantor’s Theorem which proves that the number of different cardinalities of infinite sets is also infinite! It is a little more difficult than the first article, but not so bad if you take your time with it.
September 15, 2007 at 11:11 pm |
I use the auditorium. If everyone is sitting in his/her own seat, no one is standing, no one is empty… I think it is how I was taught…
September 15, 2007 at 11:18 pm |
An infinite auditorium? Hmm…
September 16, 2007 at 4:06 pm |
Ah, no, not infinite. All I am working towards is the idea that two sets (people and seats) can be shown to have the same size (cardinality) if their members can be placed into 1-1 correspondence. No empty chairs? No people standing? We don’t have to count to know that N(people) = N(chairs)
September 16, 2007 at 4:17 pm |
ah, got it.
Perhaps this is what musical chairs is supposed to teach little children. 
January 3, 2008 at 5:39 am |
I think it is difficult for children to understand what is infinity. They have to be at least 15-16 years old.
January 3, 2008 at 10:22 am |
I kind of disagree with that, Math. I think a lot of gifted kids, at least, have a pretty good understanding of infinity well before 15 years of age. It is a very abstract concept, but some kids are ready to handle it.
March 12, 2008 at 1:00 am |
[...] even integers is equal to the cardinality of all the integers. (For more on this, check the links here.) Yet, intuitively we know that the answer must be 1/2. There’s a fascinating discussion of [...]