How about...

"Nan" is a string representation of the floating point literal NaN. Like all string representations of floating point numbers it may be treated as it's numeric value.

However, "not a number" is a non floating point string, so is treated as 0.

Gaak! Trying to say this succinctly is a great way to twist your brain into knots.

Disclaimer: IANALL, but I've played one in several companies.<grin/>