Why is division by zero impossible?

Conceptually, I don't get it. When you divide by zero, is the result "infinity" or "undefined" or what?

Please help me acheive satori, /sci/.

Division is defined by multiplication. a/b is equivalent to a*b^-1 so if you want to divide by 0, b^-1 would have to be equal to 0. However, there is no value for b that would make it equal to 0 so therefore a solution does not exist and division by zero is undefined.