4 ms·

> The other kinds of infinity - cardinals, for example - are encountered early on, and there are things you can do with them. There's plenty you can do with or

> The other kinds of infinity - cardinals, for example - are encountered early on, and there are things you can do with them. There's plenty you can do with ordinals too! Being able to interate a function transfinitely many times can be quite useful. > So, I might be biased in that, but I think that the cardinals are the most playful type of infinity. Definitely disagree. Once you know the basics, doing things with cardinals tends to be either boringly easy or impossibly hard. Ordinals, on the other hand, you can just play around with and actually get somewhere.

romwell 8y ago
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! >There's plenty you can do with ordinals too Any examples that you could introduce to a kid who just asked you "What is infinity?" - genuinely curious.
- Sniffnoy 8y ago
  > 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-countable-ordinals-part-1/ https://johncarlosbaez.wordpress.com/2016/06/29/large-counta... https://johncarlosbaez.wordpress.com/2016/07/04/large-countable-ordinals-part-2/ https://johncarlosbaez.wordpress.com/2016/07/04/large-counta... https://johncarlosbaez.wordpress.com/2016/07/07/large-countable-ordinals-part-3/ 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.

romwell 8y ago

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! >There's plenty you can do with ordinals too Any examples that you could introduce to a kid who just asked you "What is infinity?" - genuinely curious.

Sniffnoy 8y ago
> 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-countable-ordinals-part-1/ https://johncarlosbaez.wordpress.com/2016/06/29/large-counta... https://johncarlosbaez.wordpress.com/2016/07/04/large-countable-ordinals-part-2/ https://johncarlosbaez.wordpress.com/2016/07/04/large-counta... https://johncarlosbaez.wordpress.com/2016/07/07/large-countable-ordinals-part-3/ 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.