So I was reading a a question and top comment on math stack exchange that didn't make sense to me.
you can measure the temperature of something, but you can't count it. Incidentally, I claim cardinality is not the relevant feature: I would describe a random variable taking values in, say, the set of all subsets of $N$ as still discrete, even though the set of all subsets of $N$ is uncountable!
where discrete refers to:
discrete: (of a variable or data) assuming a value from a finite or countably infinite sample space;
It isn't clear to me what this means? I'd love the physical intuition or at least an example behind this?