I got a comment from Allen Knutson on the 2nd project recommending using “The Cat in Numberland” to talk about infinity with kids. I ordered the book immediately and had the boys read it a few times this week. We got around to talking about it this afternoon.

Here’s their initial reaction to the book:

In the last video we I asked the boys for 3 ideas from the book that they wanted to talk about. They chose:

(1) When “Hilbert’s Hotel” is full, how do you fit one more person in?

(2) How about fitting in 26 more people?

(3) When you take away half the people how can the hotel still be full?

Here’s the explanation for part 1 – the idea here shows one strange thing about infinity!

Here’s part 2:

My older son got a little confused by the numbering of the hotel rooms in this video. The numbering of the rooms is hardly the main point, but it is nice to be able to review / revisit some counting ideas in this unusual context:

For part 3 we had a nice conversation about how you can form a bijection between the counting numbers and the non-negative even integers. That conversation went pretty fast so I asked the boys to each find another bijection and got really lucky when they picked two pretty cool ideas – powers of 2 and prime numbers.

The last movie ended with a question about whether or not the primes were infinite. This was also hardly the main point of the project, but turned out to be a fun way to end the conversation today.

So, thanks to Allen Knutson for pointing me to the book and to Kelsey Houston-Edwards for the Infinity video which has now led to three fun projects with the boys!