Division by Zero
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.
- L'Hôpital's Rule: while $\dfrac 0 0$ is undefined, the limit of a rational function whose denominator approaches $0$ is not necessarily undefined.
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.
Mahāvīrāchārya 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.