possible tetration extension part 3 Shanghai46 Junior Fellow Posts: 20 Threads: 6 Joined: Oct 2022 10/26/2022, 08:20 PM (10/22/2022, 09:29 PM)bo198214 Wrote: (10/22/2022, 04:42 PM)Shanghai46 Wrote: Technically I don't think so Come on, be a bit more elaborative! It should be in your interest to make your finding more understandable! Let me reiterate: you write (10/21/2022, 08:29 AM)Shanghai46 Wrote: $${^r}x=\lim_{n\rightarrow~+\infty}({\log_x}^p( g^n(((f^n({^m}x)-\tau)/\lambda^k)+\tau)))={^{m-k-p}}x$$    Where r=m-k-p, r is any real number (not equal to any whole negative numbers below -1), m and p are natural numbers and k any real integer number which |k|<1.  This formula is not defining $${^r}x$$ in a unique way (apart from the typo "k any real integer number" - what you mean is "k any real number"), because for different choices of m and p we get different results. Say x=2 and r=0.9; when we choose m=p=2 then $${^{0.9}}2\approx$$ 1.8482158 m=p=3 then $${^{0.9}}2\approx$$ 1.8802187 m=p=4 then $${^{0.9}}2\approx$$ 1.8802194 (which btw seems to be an error in your given value 0.9109247189 which is not $${^{0.9}}2$$ but $${^{-0.1}}2$$ because $$1={^0}2 < {^{0.9}}2 < {^1}2 =2$$ ) So to make it a proper definition (that does not depend on the choice of m and p), I suggested to take the limit $$m=p\to\infty$$ which would be just the execution of what you described in text form in the beginning. So I am wondering a bit why you reject this formula. For simplicity lets just assume that \(0

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