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 ?

  • 5
    $\begingroup$ You can add $1^{\infty}$ and $0^0$ to that list. $\endgroup$
    – JimmyK4542
    Dec 19, 2015 at 1:03
  • 1
    $\begingroup$ There's also $\infty - \infty$, $\infty^0$ $\endgroup$ Dec 19, 2015 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, 2015 at 6:34

2 Answers 2


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?

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Just in case this turns out to be helpful:

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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.

  • $\begingroup$ L'Hospital can only be used in indeterminate formats \frac{0}{0} and \frac{\pm\infty}{\pm\infty} $\endgroup$
    Sep 1 at 9:42
Here are 7 indeterminate forms involving 0, 1, and ∞ that arise when evaluating limits

enter image description here

— Fermat's Library (@fermatslibrary) December 24, 2020

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


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