Yep, there are many counter-intuitive aspects to the rational numbers. They're ordered just like the integers, and yet given any fraction there isn't a well-def

Yep, there are many counter-intuitive aspects to the rational numbers. They're ordered just like the integers, and yet given any fraction there isn't a well-defined "next" fraction. But there are still "gaps" (irrational numbers). The same fraction has infinitely many representations. Despite that there are no more rational numbers than integers, yet the number of "gaps" far exceeds either of these. Not every fraction even has a finite decimal expansion. And fractions allow you to specify a level of precision for measurements that could never be achieved in the real world under any circumstances, which immediately raises questions about what these extraordinarily precise fractions actually refer to in the real world. I honestly believe that lots of kids detect these issues on some level, but their curiosity and confusion remain unresolved, possibly for life.