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 Generalized arithmetic operator hixidom Junior Fellow Posts: 20 Threads: 3 Joined: Feb 2014 03/11/2014, 11:20 PM (03/11/2014, 10:49 PM)MphLee Wrote: These are not the "natural" (left-associative) hyperoperations family, and seems that are different from lower hyperoperations too. Why you chose this kind of bracketing? I'm not familiar with the difference between left- and right-associative hyperoperators. I would say that the unary version is definitely righ-associative, as $[x][y][z]a=[x]([y]([z]a))$ but perhaps that is not what you are referring to. If I had to write a recursion relation along the lines of what has been posted so far, I would say it is: $a[x]b=(a[x]\frac{b}{2})[x-1](a[x]\frac{b}{2})$ which is neither left- nor right-associative, if I understand the meaning of that phrase. The ones that have been posted so far are $a [x] b=a[x-1](a [x] (b-1))$, and $a [x] b=(a [x] (b-1))[x-1]a$. which are very similar, with the only difference being that the [x-1] operation on the right side is flipped. But neither of these definitions result in the same [4] operator that I have. \begin{align*}a[4]2&=[3]a&=a^a\\a[4]4&=[3]^2a&=(a^a)^{(a^a)}\\a[4]8&=[3]^3a&=\left ((a^a)^{(a^a)}\right )^{\left ((a^a)^{(a^a)}\right )}\end{align*} etc. « Next Oldest | Next Newest »

 Messages In This Thread Generalized arithmetic operator - by hixidom - 03/11/2014, 03:52 AM RE: Generalized arithmetic operator - by JmsNxn - 03/11/2014, 03:15 PM RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 06:24 PM RE: Generalized arithmetic operator - by MphLee - 03/11/2014, 10:49 PM RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 11:20 PM RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 11:18 AM RE: Generalized arithmetic operator - by JmsNxn - 03/12/2014, 02:59 AM RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 04:37 AM RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 06:19 PM RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 06:43 PM RE: Generalized arithmetic operator - by tommy1729 - 03/21/2014, 10:31 PM RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:06 AM RE: Generalized arithmetic operator - by tommy1729 - 03/22/2014, 12:13 AM RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:42 AM RE: Generalized arithmetic operator - by hixidom - 06/11/2014, 05:10 PM

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