I’m currently working on some nice formulas that require l’Hopital’s Rule (sometimes written as l’Hospital (with the “s” silent. The “o” also goes with a “hat”) and came across a note from Professor Stephen A. Fulling, in which he mentions the never-ending zero-to-the zero power controversy.
Not even mathematicians agree on what the result should be. It has been argued that the answer is a matter of convenience, an element controversial -if not contrary- to Mathematics. What’s your take on the issue?
To learn more about the l’Hopital’s Rule and when it should be applied, see Wikipedia or WolframMathWorld.
I guess it is just a hidden double-limit problem.
Guillaume François Antoine, Marquis de l’Hôpital, was of French High Nobility under king Louis XIV aka “The Sun King”. World that died 85 years after L’Hôpital’s death. This period is the start of the transition between two periods of France. That is why his name was written Hospital the old Latin way or Hôpital the new French way.
No wonder also this man could think of limit of worlds like 0/0 or 0⁰.
The point is the ambiguity of the question. Newton and Leibnitz have fought for years for the ambiguity of the question. Leibnitz even died of it. The notation is ambiguous because their is no clear decision on which the priority is given to the power or the powered. When we will have such clear writing we will know.
Look at this we can’t even agree on 2^3^4
https://plus.google.com/u/0/104277466162910953762/posts/e3jCt51VfmD
Thank you for stopping by and for the historical context.
I looked at the controversy discussed in the plus.google.com link provided and tend to agree with the poster that goes by the name of Eirik Albrigtsen when said poster states that and quote:
“The point here is that certain solutions gets the associativity wrong when it’s done implicitly”.
Certainly, the problem there is on the ambiguity caused by software implementing associative rules. However, I don’t see how that ambiguity is relevant to the 0^0 controversy as in this case there is no associative ambiguity concerns. We simply take a single number, 0, and raise it to 0.
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