Why Is 0/0 Considered Indeterminate If Division by Zero Is Undefined

[Suyogya]

how can 0/0 be indeterminate form if division by zero is undefined. The expression 0/0 rather be undefined.

 

[Mark44]

how can 0/0 be indeterminate form if division by zero is undefined. The expression 0/0 rather be undefined.

That's correct -- $\frac 0 0$ is not defined. Indeterminate forms always arise in the context of limits such as $\lim_{x \to 0} \frac {2x} x$. This limit has the form of $\frac 0 0$, but that is not saying that $\frac 0 0$ is a meaningful answer.

Some textbooks write indeterminate forms in brackets, such as $[\frac 0 0 ]$ or $[\frac \infty \infty ]$, just to emphasize that they don't intend that these forms be interpreted as numbers.