On: NaN does not equal NaN

The most intuitive way to describe this for me is:

You've got 2 things, but you know nothing about them. Does the fact that you know nothing about them alone make them equal?

True, they have a commonality (you know nothing about them) but that's not enough to make them equal.

Yes, and the creators of the concept were kind enough to embed this intuition into the name, just so you can't forget.

All you know is what it is NOT, not what it IS. So you can't tell if it's the same as anything else.