# List of Indeterminate forms in Mathematics

I know that ,

$1) \frac{0}{0}$

$2) \frac{\pm\infty}{\pm\infty}$

$4) 0 \times(\pm\infty)$ are Indeterminate forms.

But in measure theory $0 \times(\pm\infty) =0$

Are there any other indeterminate forms ? And Why ?

• You can add $1^{\infty}$ and $0^0$ to that list. Dec 19, 2015 at 1:03
• There's also $\infty - \infty$, $\infty^0$ Dec 19, 2015 at 4:23
• "Indeterminate form" really shouldn't be taken to have a hard, well-defined meaning. Division by zero and general arithmetic with infinity is not allowed by the rules of algebra. "Indeterminate forms" are just expressions which naively substitute a limiting value for the limit variable. Dec 19, 2015 at 6:34

The following is a list of indeterminate forms usually encountered:

$$\frac{0}{0}$$ $$\frac{\infty}{\infty}$$

$$0 \cdot \infty$$ $$0^0$$ $$\infty - \infty$$ $$\infty^0$$ $$1^\infty$$

Why are they indeterminate? Just in case this turns out to be helpful: The sources of these images are: 1. https://www.math.brown.edu/~pflueger/math1a/lecture24.pdf

In case, you are starting off learning about indeterminate forms I suggest taking a look at the pdf above. Hope this helps.

Here are 7 indeterminate forms involving 0, 1, and ∞ that arise when evaluating limits — Fermat's Library (@fermatslibrary) December 24, 2020

These are popularly known as the seven deadly sins of calculus.