Part 2 of talking about infinity with my younger son

Yesterday my younger son and I talked about why the set of rational numbers has the same size as the set of positive integers. That project is here:

https://mikesmathpage.wordpress.com/2021/01/30/talking-about-infinity-with-my-younger-son/

Today we followed up on that project by taking a look at why the set of real numbers is larger. First, though, I wanted to tie up one loose end from yesterday. Unfortunately, though, I left things a little too open ended and we didn’t tie up that loose end in one video:

Now that we understood that we’d over counted (in some sense) yesterday, I wanted to show him why that over counting didn’t really change the proof. I also wanted to show him one real curiosity that comes up with infinite sets:



Now we moved on to talking about real numbers. I suspected that he’d seen Cantor’s diagonal argument before (and he had), so I asked him to sketch the proof. He got most of the way there:



Finally, we tied up the loose ends from his summary of Cantor’s diagonal argument and talked about one other surprise with infinite sets.

We had a great time talking about infinity this weekend. It amazes me that kids can get their heads around ideas in math that were absolutely cutting edge just over 100 years ago!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s