Edit: I’ve only now learnt that these are also terms from economics, on which I don’t know much; Since they’re adopted from the mathematical ones, I’m going to assume my comment still has some useful content and leave it up.
Only referring to the first paragraph, because mathematically it’s very wrong:
Ordinal numbers are ranked. In contrast, cardinal numbers are equidistant.
Equidistant in what way? How are ordinal numbers not equidistant in the same way? And how is that a contrast to being ranked? Distance and order are unrelated.
So you can do mathematical operations on cardinal numbers, but not ordinal
Yes this is the conventional usage in economics, not its abstraction in mathematics. The crux of my argument is that welfare values are not directly observable.
Edit: I’ve only now learnt that these are also terms from economics, on which I don’t know much; Since they’re adopted from the mathematical ones, I’m going to assume my comment still has some useful content and leave it up.
Only referring to the first paragraph, because mathematically it’s very wrong:
Equidistant in what way? How are ordinal numbers not equidistant in the same way? And how is that a contrast to being ranked? Distance and order are unrelated.
Sure you can:
https://en.wikipedia.org/wiki/Ordinal_arithmetic
Yes this is the conventional usage in economics, not its abstraction in mathematics. The crux of my argument is that welfare values are not directly observable.