Reductio ad absurdum – Why can’t one divide by 0?

If $\frac{1}{0}=a$, i.e. there were a number like this, you could find out by transforming → $1=0●1$, which cannot be the case. 

There is no number a, such that when multiplied by 0 the result is 1. The assumption that $\frac{1}{0}$ would have a result a, leads to a contradiction!

In mathematics, this procedure is called a mathematical proof. This particular one is a reductio ad absurdum (“reduction to absurdity”).