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 Tetration of 0^0^0 .... or h(0)=? andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/19/2007, 07:27 AM (This post was last modified: 11/19/2007, 04:41 PM by andydude.) To answer your specific question, you should probably read either Knoebel's Exponentials Reiterated or McDonnell's Some Critical Points of the Hyperpower Function since they both talk about this. Near zero, $h(x) = {}^{\infty}x$ can be defined in one of three ways: as the limit of odd towers as the height tends to infinity (giving $h_O(0) = 0$), as the limit of even towers as the height tends to infinity (giving $h_E(0) = 1$), or as the inverse function of $f(x) = x^{1/x}$ (giving $h_I(0) = 0$). Each one of these definitions gives a different answer as x approaches 0. The strange thing is that all definitions are equivalent for $e^{-e} < x < e^{1/e}$. Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Tetration of 0^0^0 .... or h(0)=? - by Ivars - 11/18/2007, 10:26 AM RE: Tetration of 0^0^0 .... or h(0)=? - by Gottfried - 11/18/2007, 05:29 PM RE: Tetration of 0^0^0 .... or h(0)=? - by Ivars - 11/18/2007, 05:56 PM RE: Tetration of 0^0^0 .... or h(0)=? - by andydude - 11/19/2007, 07:27 AM RE: Tetration of 0^0^0 .... or h(0)=? - by Ivars - 11/19/2007, 10:52 AM

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