Actually, the question is which definition of 'the reals' is it using. For the true mathematical reals, sqrt(-1) is a domain error, so an error message would be appropriate. Only when you extend the reals to add the Not-a-Number value, can you include that in the possible results. Since SQL predates the IEEE-754 definition for floating-point representations, which is as far as I know the origin of the NAN value, at least as far as a general definition. it isn't surprising that it adopted some conventions that disagree with the later standard.