NaN is unordered, so the numerical comparison operators <, <=, >, and >= return false if either or both operands are NaN (�15.20.1). The equality operator == returns false if either operand is NaN, and the inequality operator != returns true if either operand is NaN (�15.21.1). In particular, x!=x is true if and only if x is NaN, and (x<y) == !(x>=y) will be false if x or y is NaN.
JLS Floating-point operators produce no exceptions (�11). An operation that overflows produces a signed infinity, an operation that underflows produces a denormalized value or a signed zero, and an operation that has no mathematically definite result produces NaN. All numeric operations with NaN as an operand produce NaN as a result. As has already been described, NaN is unordered, so a numeric comparison operation involving one or two NaNs returns false and any != comparison involving NaN returns true, including x!=x when x is NaN.
JLS Also the API for the Math class