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.

Note

While $\dfrac 0 0$ is undefined, the limit of a rational function whose denominator approaches $0$ is not necessarily undefined (see L'Hôpital's Rule).

Sources

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 1.3$