You only get NaN for division by zero if you divide 0 by 0 in IEEE floating point. For X/0 with X ≠ 0, you get sign(X)•Inf.
And for real numbers, X/0 has to be left undefined (for all real X) or else the remaining field axioms would allow you to derive yourself into contradictions. (And this extends to complex numbers too.)
I have a strong relationship to what you get when you divide by zero.
Good ol’ NaN
You only get NaN for division by zero if you divide 0 by 0 in IEEE floating point. For X/0 with X ≠ 0, you get sign(X)•Inf.
And for real numbers, X/0 has to be left undefined (for all real X) or else the remaining field axioms would allow you to derive yourself into contradictions. (And this extends to complex numbers too.)