Not-a-Number definition mathematics
(NaN) An IEEE floating point representation for the result of a numerical operation which cannot return a valid number value. A NaN can result from multiplying an infinity by a zero, or from subtracting one infinity from another [what else?].
NaN is encoded as a special bit pattern
[what pattern?] which would otherwise represent a floating-point
number. It is used to signal error returns where other mechanisms are not convenient, e.g. a hardware floating-point unit
and to allow errors to propagate through a calculation.
Similar bit patterns represent positive and negative overflow
and the positive and negative infinities resulting from division by zero.
Bit patterns (http://psc.edu/general/software/packages/ieee/ieee.html).
[ANSI/IEEE Std 754-1985].