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 Operations with fractional index between + and * ? andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 10/21/2009, 01:30 AM (This post was last modified: 10/21/2009, 01:31 AM by andydude.) So I checked up on it, and no, it is not the case. Also, I have some bad news. If we assume the Schroder functions (accordingly, the Abel functions) are iterated exponentials, then that means that the associated hyperoperation hierarchy would have the recursion rule: $HE_n(x, y) := \exp(HE_{n-1}(\log(x), y))$ which (if n=2 is multiplication) requires that (n=1) is $HE_1(x, y) = x + \log(y)$, which is not addition, so this scheme does not form a hyperoperation hierarchy. However, if I might draw your attention to the Tetration Ref. section 2.3.4, the recursion rule: $HR_n(x, y) := \exp(HR_{n-1}(\log(x), \exp^{n-3}(y)))$ has many of the same characteristics, and satisfies addition (n=1), mul (n=2), and powers (n=3). The only difference is in the heighest exponent. $HR_n(x, y) = HE_n(x, \exp^{\circ\left({n-2 \atop 2}\right)}(y))$ « Next Oldest | Next Newest »

 Messages In This Thread Operations with fractional index between + and * ? - by Gottfried - 10/09/2009, 08:38 PM RE: Operations with fractional index between + and * ? - by Gottfried - 10/10/2009, 12:11 AM RE: Operations with fractional index between + and * ? - by bo198214 - 10/15/2009, 08:44 PM RE: Operations with fractional index between + and * ? - by andydude - 10/17/2009, 09:20 PM RE: Operations with fractional index between + and * ? - by Gottfried - 10/17/2009, 09:41 PM RE: Operations with fractional index between + and * ? - by andydude - 10/20/2009, 08:42 PM RE: Operations with fractional index between + and * ? - by andydude - 10/21/2009, 01:30 AM

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