NaN doesn't represent a number that doesn't exist, it represents a value that hasn't been computed because the computation yielded an error which wasn't handled

NaN doesn't represent a number that doesn't exist, it represents a value that hasn't been computed because the computation yielded an error which wasn't handled yet. Imagine having error values (or exception objects) that get allocated every time an error happens. You don't expect necessary to be able to compare two instances of an exception object, instead you'll call a function that will tell you e.g. which type of error it is. Now, NaN are not really quite like that. For one, it's unusual to stuff the error object in the same place as the actual value and also treating it as if it was the same type as the value. Furthermore reassigning the error object into another variable implicitly "clones" it into a new identity. It's possible to imagine an alternate universe where each arithmetic operation that produces a NaN allocates a new unique number (there are many available bits so that you'll get quite far without a wrap around. But the additional complexity in hw was deeped not worth it.