Undetermined vs. Undefined This often comes up in precalculus and calculus, that is sometimes an expression will be said to undefined while at other times undetermined. What is the fundamental difference between the two? For example, division by zero $x/0$ is said to be undefined, while $0/0$ is said to be undetermined.

Division by zero is undefined in every case.

In calculus, the phrase “$0/0$ is an indeterminate form” means that you have a limit of the form $$ \lim_{x\to a}\frac{f(x)}{g(x)} $$ where $$ \lim_{x\to a}f(x)=0 \qquad\text{and}\qquad \lim_{x\to a}g(x)=0 $$ but $f(x)/g(x)$ is defined in a set having $a$ as a limit point (usually, but not necessarily, a punctured neighborhood of $a$) and nowhere you do $0/0$, which makes no sense. In this case you can apply no standard theorem on limits and the limit, if existing, must be computed with some different technique than simply substituting the value $a$.

Some say that the value of the _fraction_ $0/0$ (no reference to limits) is undetermined, but this has no real usefulness.