Actually, there is a concept in mathematics known as “unity” values. These values are extensions that are carefully constructed to reconcile outlying problems in a system. For example, you can think of ring at infinity in the complex plane as being a point or a set of points, and some formerly pretentious problems go away. There are other examples of this with respect to cardinalities of sets where you can demonstrate that you can pick the structure of the continuum of infinities so long as |P(A)| > |A| and nothing breaks.
DISCLAIMER: I am only working with my vague memory of my some interesting caveats during my math studies. I apologize if I did a woeful job of representing the concepts I alluded to above.
If you want to believe that NaN is a solitary value, then you are probably going to be unhappy with some of the results like the equality operator not working the way you expect/want. However, if you choose to believe that NaN is more of a continuum of “badness” represented by a solitary placeholder, then you are perfectly happy with the behavior of the equality operator. In other words, you lose sight of the fish you caught in the sea but you catch another that looks the same but is just as smelly.
