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What about imaginary numbers?



You can still compare them, e.g two numbers could or couldn't be equal. Equality is a form of comparison


wouldn't this make all things comparable?


Except apples and oranges apparently.


You can compare apples and oranges alphabetically.


As far as I can tell, it's not that you can't compare apples and oranges, it's just often misleading.


You don't even have to do that: Just well-order the universe and use the resulting ordering for your less-than operator.


1 != sqrt(-1). That's an example of a comparison between a real number and an imaginary number.




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