in reply to zero to the power zero

The counter-argument is where you use logarithms to figure out the answer.

0 ** 0 = exp ( 0 * ln(0) )
       = exp ( 0 * undef )
       = exp ( undef )
       = undef

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If you argue that exp(ln($anything)) is just $anything, you still get 1 * 0 and then a zero rseult.

So I would argue against an answer of one .. the value approaches one, but I think the actual point is a singularity.

Alex / talexb / Toronto

"Groklaw is the open-source mentality applied to legal research" ~ Linus Torvalds

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Re^2: zero to the power zero
by randyk (Parson) on Feb 18, 2007 at 23:11 UTC
    If you interpret 0*ln(0) as a limit of x*ln(x) as x tends to 0, then L'Hôpital's rule can be used to infer what this limit is (if it exists): 
      Lim  x ln(x)  = Lim  1/(1/x) ln(x)
  x->0            x->0    

                = Lim  1/(-1/x^2) (1/x)
                  x->0
 
                = Lim  -x  = 0
                  x->0

    [download]
    Thus, since the limit exists, the limit of x*ln(x) as x approaches 0 is 0.
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