I know in calculus the form $\frac{0}{0}$ is indeterminate.but if it is not calculus is it still indeterminate or undefined in the real number field?
P.S. I know that $\frac{1}{0}$ is undefined whether it is calculus or normal arithmetic in the real number system. but in the projectively extensive real number system, $\frac{1}{0}=\infty$ but in this system what would be $\frac{0}{0}$ it becomes $0*\infty$ also an indeterminate form. in that system the problem $\frac{1}{0}$ is solved but $\frac{0}{0}$ remains.
P.P.S some answers in the question which has been identified as a duplicate of my Q state the $\frac{0}{0}$ is indeterminate. but in Wikipedia page(division by zero) states it is undefined. and that question was asked not to clarify this ambiguity(indeterminate or undefined) and there is no clear answer to my problem.
Unlike $0\cdot\infty$, which is 0 if it's zero measure times infinite value (or zero value times infinite measure ) but otherwise not defined, one never attributes a value to $0/0$. It's BOTH indeterminate AND undefined.
To be specific it's indeterminate because if you tried to give a meaning to it, you could justify anything. It's undefined because (unlike with $0\cdot\infty$) one doesn't define it by convention either.