What? NaN is actually a number in the sense of being in the domain of the floating-point type. You seem to be mixing up "not a number" (as in character string or list) versus "not a number" as in a special IEEE representation that has special uses in numeric code.

A floor function that returns NaN when given a string, instead of throwing a type mismatch exception, is crap design, and a strawman example of that type of checking. It's not an appropriate use of NaN!