# Division by Zero

## Mistake

Let $x$ and $y$ be numbers such that $y = 0$.

The quantity $\dfrac x y$ is undefined.

It is a common mistake to forget this fact when evaluating formulas.

## Historical Note

Brahmagupta stated that:

positive or negative divided by cipher is a fraction with that for denominator.

This was then referred to as quantity with zero as denominator.

Mahaviracharya writes in Ganita Sara Samgraha of c. $850$ CE:

A number multiplied by zero is zero and that number remains unchanged which is divided by, added to or diminished by zero.

which is of course seriously questionable.