> Sure, oridnals are interesting, but in the context of explaining infinity to kids transfinite induction is probably not the easiest thing to throw into the fun basket. Even first-year undergrads often have to learn regular induction!
Sure, but do you really have to explain that?
When I imagine introducing kids to ordinals, like the OP talks about, I'm assuming it's basically taking the approach in, say, John Baez's blog posts on large countable ordinals[1].
[1] https://johncarlosbaez.wordpress.com/2016/06/29/large-counta... https://johncarlosbaez.wordpress.com/2016/07/04/large-counta... https://johncarlosbaez.wordpress.com/2016/07/07/large-counta...
> Any examples that you could introduce to a kid who just asked you "What is infinity?" - genuinely curious.
Hm, maybe not. Maybe some of the classic examples of weird things that can happen with transfinite-time processes... but explaining any of that might be hard. And also that might not really be the right time to introduce people to discontinuity.
Really like I said I was basically thinking of the approach above, without application. I think it stands on its own pretty well, it's fun, you can play around with it -- it's basically the "is too, times infinity+1!" game except formalized (so it kind of comes naturally out of something kids already try to do) -- and the questions have actual answers.