1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

1 to infinite

  1. Aug 24, 2006 #1
    Why is [tex]1^ \infty [/tex]. undefined?
    Last edited by a moderator: Aug 24, 2006
  2. jcsd
  3. Aug 24, 2006 #2


    User Avatar
    Homework Helper

    This has been discussed here recently. The gist is that [itex]1^\infty[/itex] can only be interpreted as standing for a class of limit expressions, including the following:

    [tex] \lim_{x \rightarrow \infty} 1^x = 1[/tex]

    [tex] \lim_{x \rightarrow \infty} (1+\frac{1}{x})^x = e[/tex]

    [tex] \lim_{x \rightarrow \infty} (1+\frac{1}{x})^{x^2} = \infty[/tex]

    Since these don't all have the same limit (as opposed to, say, the limit expressions corresponding to [itex]0/\infty[/itex]), we can't assign a value to [itex]1^\infty[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?