- NaN is a floating point number, and NaN != NaN by definition in the IEEE 754-2019 floating point number standard, regardless of the programming language, there's nothing JavaScript-specific here.
- In JS Number.isNaN(v) returns true for NaN and anything that's not a number. And in JS, s * n and n * s return NaN for any non empty string s and any number n ("" * n returns 0). (EDIT: WRONG, sée below)
No? It is easy to verify that `"3" * 4` evaluates to 12. The full answer is that * converts its operands into primitives (with a hint of being number), and any string that can be parsed as a number converts to that number. Otherwise it converts to NaN.
Therefore, trying to do math with either (for example: NaN/NaN or inf./inf.) was to try to pin them down to something tangible and no longer conceptual — therefore disallowed.
This is not about infinity in math not being a _specific_ value, it can certainly be (the actual infinite instead of potential).
It's simply about design and foresight, in my humble opinion.