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?