# Temperature is discrete but not countable? [closed]

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?

• I think you're confused because you think counting is the same as measurement, right? But actually, counting is an act of assigning natural numbers to a sequence of objects. One, two, three, ... Commented Jun 1, 2023 at 5:07
• Yes but i can assign each measurement a natural number too right? Would love if you could elaborate? Commented Jun 1, 2023 at 5:09
• This would count your measurements, not the quantity you measure. I.e. you'll know how many measurements you've made, but not how hot the object being measured was. Commented Jun 1, 2023 at 5:10
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– Buzz
Commented Jun 1, 2023 at 21:57

Physical variables are almost never discrete, but rather continuous (although some discontinuities in Physical systems may exist). Same for the temperature,- it's from the real number domain $$T \in [0; T_P] \approx [0; 10^{32}K]$$. So countability is not applicable here.