# Grown-ups and Infinity

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.

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…

An infinite auditorium? Hmm…

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)

ah, got it. 🙂 Perhaps this is what musical chairs is supposed to teach little children. 😉

I think it is difficult for children to understand what is infinity. They have to be at least 15-16 years old.

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

isa very abstract concept, but some kids are ready to handle it.The typical volume really is as tracks:3 005 thousand located in locate matters,362 million located in commodity as well as One particular 714 million within trades just about entirely located in Over-the-counter sales,