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 Generalized arithmetic operator tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 03/21/2014, 10:31 PM https://sites.google.com/site/tommy1729/...e-property We use a uniqueness condition on sexp : for x,y >=0 : sexp(x+yi) is real entire. We could change the base e to base 2 or change tetration to pentation to generalize things. Imho that is the way to do hyperoperation and I believe that answers almost all questions. ( I read your paper ). Imho there are 2 big questions remaining : 1) informally speaking : what lies between tetration and pentation ? Once again I mean the " half-super functions " as has been discussed on this forum before ( mainly by myself and James Nixon ). Let S mean "superfunction of ..." and S^[-1] "is the superfunction of ..." We have S^[-1](f(x)) = f ( f^[-1](x)+1) examples : S(exp(x)) = sexp(x) S^[-1](sexp(x)) = sexp(slog(x)+1) = exp(x) Question : if we say S^[a+b](f(x)) = S^[a](S^[b](f(x)) = S^[b](S^[a](f(x)) Then what is S^[1/2](f(x)) ? Or what is S^[1/2](exp(x)) ? (Question 2 is still under investigation and not formulated yet) regards tommy1729 « 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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