What is the rationale for all comparisons returning false for IEEE754 NaN values?

Question

Why do comparisons of NaN values behave differently from all other values? That is, all comparisons with the operators ==, <=, >=, <, > where one or both values is NaN

Answer 1

NaN can be thought of as an undefined state/number. similar to the concept of 0/0 being undefined or sqrt(-3) (in the real number system where the floating point lives).

NaN is used as a sort of placeholder for this undefined state. Mathematically speaking, undefined is not equal to undefined. Neither can you say an undefined value is greater or less than another undefined value. Therefore all comparisons return false.

This behaviour is also advantageous in the cases where you compare sqrt(-3) to sqrt(-2). They would both return NaN but they are not equivalent even though they return the same value. Therefore having equality always returning false when dealing with NaN is the desired behaviour.