I know the importance of continuous sets in the study of statistics as a branch of math. But I don't know of any measurements that can't be represented by integer multiples of a unit for all practical purposes. And the students in the non-calculus stats course can't grasp what continuity is anyway.
> But I don't know of any measurements that can't be represented by integer multiples of a unit for all practical purposes.
You can always discretize any real number, but why would you? I don't see how integers are easier to deal with than real numbers. Calculus can be viewed as the limit in which you discretize numbers infinitely finely. Once you know how things work in that limit, it's generally easier to use calculus than to work with discretized quantities. One example: summations are often more difficult than integrals, and one way of approximating sums is to turn them into integrals.
From my perspective, calculus is a basic part of mathematics that everyone should be expected to learn in school. In the US, calculus is often viewed as some sort of intimidating subject that only extremely clever people can grasp, and then only in late high-school or in university, but in East Asia, it's taught to children as a matter of course.
I know the importance of continuous sets in the study of statistics as a branch of math. But I don't know of any measurements that can't be represented by integer multiples of a unit for all practical purposes. And the students in the non-calculus stats course can't grasp what continuity is anyway.