If something is undefined in math, it doesn't mean define it with whatever value you want: it means undefined because you can't define it. The function sqrt(x)

If something is undefined in math, it doesn't mean define it with whatever value you want: it means undefined because you can't define it. The function sqrt(x) is undefined for negative x in the real number system. Is it therefore zero? No. Just because a value is not in a domain doesn't mean just pick one. Most math textbooks I know and Wikipedia define division as the inverse of multiplication. You are saying that there is a distinction, the inverse of multiplication is not the same as division: you can write 1/0, but that is not the same as 1 * 0⁻. This is unconventional to say the least, and the only argument you give to make this destinction is your desire to define 1/0 as 0.