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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

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    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].
     
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