There are seven expressions commonly considered as indeterminate forms: $\frac{0}{0}$, $\frac{\infty}{\infty}$, $0\times \infty$, $\infty -\infty$, $0^{0}$, $1^{\infty}$ and $\infty^{0}$; since as I understand, they can all equal more than one thing dependant on the situation.
- How were these discovered/defined as the base cases?
- Aren't some of them the same expression with little manipulation? ($\frac{\infty}{\infty} = \frac{1}{\infty}\times \infty = 0\times\infty$)
- Does the defining of them actually matter apart from recognising when you have to be careful determining a limit?