Dividing by Zero

Dear sci/math,

I have a problem i would like to understand. Everybody knows you can't divide by zero, like everybody knows that binary codes just consist of 0 and 1.
First question: Why do you take a variable that is not defined at
for such an important system?

Second question: Would there be any difference if zero was defined for the casual use of Computers?

Maybe someone can help me just imagining how zero could be defined a little, if my questions make too little sense.

Thanks anon.

>>13
Well that's why we actually call it zero, not nothing.  The empty set, or no solution, is more what you want if what you want is nothing.