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Generalized arithmetic operator
#12
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
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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 hixidom - 03/22/2014, 12:42 AM
RE: Generalized arithmetic operator - by hixidom - 06/11/2014, 05:10 PM

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