Not a bad idea at all. You can have a separate class called “Arithmetic” and that can be used to learn arguably the most boring application of mathematics: operations on numbers. Maybe distinguishing mathematics from arithmetic will make people hate the subject less. Set theory alone you can get to continuum hypothesis. I’m sure children would find the idea that some infinite sets are bigger than other infinite sets quite fascinating.

> Set theory alone you can get to continuum hypothesis.

Ironically, her independence from ZF would make the classical Bourbaki group shiver. The same way the earlier, better known, work of Goedel did.

I don't know, if you are aware of Bourbakis spirit. There is something much more important in this context as the content-wise difference between sets and numbers. I never would argue against applying naive set definitions in a suiting way. But Bourbaki had an agenda, and this agenda is not for everyone (certainly not for me).

I'm the right age to have done New Math [1] in my first years at school, my memory of it is that it seemed fine but at age five I wasn't really thinking about comparing different educational styles.

[1] https://en.wikipedia.org/wiki/New_Math

> Kindergarten starts math education with set theory.

Well what’s wrong with that?

Emphasis on 'theory', not 'set'.