0
$\begingroup$

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 ?

$\endgroup$
  • 3
    $\begingroup$ You can add $1^{\infty}$ and $0^0$ to that list. $\endgroup$ – JimmyK4542 Dec 19 '15 at 1:03
  • 1
    $\begingroup$ There's also $\infty - \infty$, $\infty^0$ $\endgroup$ – Omnomnomnom Dec 19 '15 at 4:23
  • 3
    $\begingroup$ "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. $\endgroup$ – Tac-Tics Dec 19 '15 at 6:34
3
$\begingroup$

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?

enter image description here

Just in case this turns out to be helpful:

enter image description here

The sources of these images are: 1. https://www.math.brown.edu/~pflueger/math1a/lecture24.pdf

  1. http://17calculus.com/limits/indeterminate-forms/

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

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.