Question

Why?

1. By the IEEE-754 standard, NaN (Not-a-Number) represents an undefined or unrepresentable value (for example, the result of 0/0 or sqrt(-1)).
2. The standard defines all comparisons with NaN as unordered. In particular, equality comparisons involving NaN always evaluate to false. So NaN == NaN is false.
3. To test whether a value is NaN you must use a dedicated predicate such as isnan() (C/C++), Number.isNaN() (JavaScript), or platform-specific functions — not equality.

Examples (behavior in common languages)

// C (IEEE-754 floating point)
double x = 0.0/0.0;          // NaN
printf("%d\n", x == x);     // prints 0 (false)
printf("%d\n", isnan(x));   // prints 1 (true)

// JavaScript
let x = NaN;
console.log(x == x);        // false
console.log(Number.isNaN(x));// true

// Python
import math
x = float('nan')
print(x == x)               # False
print(math.isnan(x))        # True