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 A new set of numbers is necessary to extend tetration to real exponents. marraco Fellow Posts: 93 Threads: 11 Joined: Apr 2011 03/19/2015, 10:45 PM (This post was last modified: 03/19/2015, 10:53 PM by marraco.) (03/19/2015, 09:59 PM)sheldonison Wrote: (03/19/2015, 12:47 AM)marraco Wrote: .... Tetration exponent product is non commutative. In general: $^n(^{\frac{1}{m}}a) \,\neq\, ^{\frac{1}{m}}(^na)$ I would also add that for analytic tetration in general: $^n(^{\frac{1}{n}}a) \,\neq a$ I defined $^n(^{\frac{1}{n}}a) \, = a$ as ttr($(^{\frac{1}{n}}a)$ ,n,1)=a were $(^{\frac{1}{n}}a)$ may be multivalued. It has some problems, like $\lim_{n \rightarrow \infty} (^{\frac{1}{n}}a) = a^{\frac {1}{a}}$, which has "a" solutions, (for a E N), against °a=1 by definition. So, it looks like this definition of $^{\frac{1}{m}}a$ is wrong all the way. Still, there should be some, non integer number t, such $c \,=\, ({^t{a}}) \,\Leftrightarrow\, ^nc\,=\, a$ « Next Oldest | Next Newest »

 Messages In This Thread A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/11/2015, 07:56 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/12/2015, 06:04 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/12/2015, 10:58 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/12/2015, 11:10 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by sheldonison - 03/14/2015, 10:37 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/19/2015, 12:47 AM RE: A new set of numbers is necessary to extend tetration to real exponents. - by sheldonison - 03/19/2015, 09:59 PM RE: A new set of numbers is necessary to extend tetration to real exponents. - by marraco - 03/19/2015, 10:45 PM

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