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Operations with fractional index between + and * ?
#7
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:



which (if n=2 is multiplication) requires that (n=1) is , 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:



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.

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RE: Operations with fractional index between + and * ? - by andydude - 10/21/2009, 01:30 AM

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