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Math Help - lim x^x

  1. #16
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    I don't agree that this discussion is tedious. I think your reply was rather tedious. Personally I don't beleive that  0^{0} := 1 , I think that this definition only holds for convenience in special cases.

    It's not hard to think of examples where  f(x), g(x) approach zero continuously, yet  f(x)^{g(x)} does not approach 1

    I'm still interested in your rigorous proof though.

    -pomp.
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  2. #17
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Moo View Post
    ... and the limit as x comes from the left : x\to 0^- ?...
    As for the function \sqrt{x} the point x=0 for the function f(x)=x^{x} is a branch point. The value of the function f(x)=x^{x} for x \le 0 are illustrated in the figure...



    Of course is...

    lim_{ x\rightarrow 0^{+}} = lim_{ x \rightarrow 0^{-}} = 1

    Kind regards

    \chi \sigma
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  3. #18
    MHF Contributor chisigma's Avatar
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    ‘Lady’ Moo : … I like the way you refer to yourself... it would be more interesting to give an outline of the proof... (I've seen some, I'm thinking about anyone who reads this…)


    pomp : … I don't agree that this discussion is tedious. I think your reply was rather tedious. Personally I don't believe that 0^{0}=1, I think that this definition only holds for convenience in special cases… I'm still interested in your rigorous proof though…

    Mi past experience about the question 0^{0}= ? suggests that for some people that is a sort of ‘tabu’ which ‘hits a nerve’… I wonder why but that is the true

    I likely accept the proposal of ‘Lady’ Moo and plomp to explain a rigorous proof of the fact that is 0^{0}=1 at only one condition: a moderator [or more than one moderator..] will assume the role of ‘impartial judge’ and will decide if from the ‘mathematical point of view’ the ‘proof’ is correct or not… is someone disposable to that?…


    Kind regards


    \chi \sigma
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