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 Tetration FAQ Discussion andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/13/2007, 08:37 AM Gottfried Wrote:a) "Tower of height n", n'th tetrate (the latter, if context of continuous operation is focused), heterogeneous, leave "nested" for some more special cases (though I have no idea actually)There are only two kinds of cases with heterogeneous towers / nested exponentials: $a^{b^c}$ as an expression, and $x \rightarrow a^{b^x}$ as a function, there are no other special cases. Even if the x is somewhere else, you can view it as the composition of nested exponential functions and other functions. Even the expression ${e^{ae^{be^c}}} = {(e^a)}^{({e^b)}^{(e^c)}}$ is just a tower (of hight 3 or 4) with weird bases. Reminds me of one paper that tried to call these expressions binary iterated powers but they're still towers to me. Gottfried Wrote:b) @Jay: top exponent, initial exponent; preferring "initial" to connect to iteration-theory("initial state") and due to the opportunity to be able to better talk about infinite towers and their fixpoints then.I've actually noticed that there is a problem with this. Lets say you have a tower of even hight n, and you want to consider a base/exponent at tower level m=n/2. For all levels > m, level m is a base. For all levels < m, level m is an exponent. So in general what can these be called, if not bases, and not exponents? I like to call them elements or tower elements, but thats just my vote. This comes up so rarely, that it may not make much of a difference. I like the idea of calling them all exponents, but just remember, they are also bases. Also, the levels have been called tower heights, if i remember right. Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Tetration FAQ Discussion - by bo198214 - 08/09/2007, 12:07 AM Literature - by Gottfried - 11/23/2007, 04:30 PM RE: Literature - by andydude - 12/17/2007, 07:31 PM RE: Tetration FAQ - by andydude - 01/13/2008, 08:43 AM RE: Tetration FAQ - by Ivars - 01/13/2008, 10:17 AM RE: Tetration FAQ - by GFR - 01/13/2008, 04:02 PM RE: Tetration FAQ - by andydude - 01/16/2008, 04:13 AM RE: Tetration FAQ Discussion - by Gottfried - 07/17/2008, 10:34 AM FAQ-discuss: What is a fixpoint? - by Gottfried - 07/17/2008, 10:45 AM FAQ-discuss: What does f o g mean? - by Gottfried - 07/17/2008, 10:47 AM FAQ-discuss: What does half-/ fractional-/continuous-/complex iteration mean? - by Gottfried - 07/17/2008, 10:48 AM RE: FAQ-discuss: What does half-/ fractional-/continuous-/complex iteration mean? - by andydude - 07/17/2008, 02:52 PM Intro and Formula sheet - by andydude - 11/13/2007, 01:21 AM RE: Intro and Formula sheet - by jaydfox - 11/13/2007, 02:39 AM RE: Intro and Formula sheet - by andydude - 11/13/2007, 03:15 AM RE: Intro and Formula sheet - by andydude - 11/13/2007, 03:25 AM RE: Intro and Formula sheet - by Gottfried - 11/13/2007, 06:08 AM RE: Intro and Formula sheet - by Gottfried - 11/13/2007, 06:12 AM RE: Intro and Formula sheet - by andydude - 11/13/2007, 08:37 AM RE: Intro and Formula sheet - by andydude - 11/13/2007, 09:09 AM RE: Intro and Formula sheet - by bo198214 - 11/13/2007, 10:42 AM RE: Intro and Formula sheet - by andydude - 11/15/2007, 03:16 AM RE: Intro and Formula sheet - by jaydfox - 11/15/2007, 03:38 AM RE: Intro and Formula sheet - by andydude - 11/30/2007, 05:32 PM [split] Tetration FAQ - by Ivars - 07/11/2008, 06:28 AM

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