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 Zeration marraco Fellow Posts: 100 Threads: 12 Joined: Apr 2011 03/20/2015, 06:11 AM (This post was last modified: 03/20/2015, 07:15 AM by marraco.) (02/19/2008, 12:24 PM)bo198214 Wrote: the bracketing must be to the right. So ao(ao(aoa))=a+4 ao(aoa)=a+3 aoa=a+2 a = a+1 ??? The answer to that question comes clear if zeration is defined this way: Neutral element: $^{-\infty \,=\, 0 - \infty \,=\, -\infty}$ $\,\,\,-\infty \,=\, a \,+\, -\infty$ $\,\,\,-\infty \circ a \,=\, a \,+\, 0$ $\,(-\infty \circ a) \circ a \,=\, a \,+\, 2$ $((-\infty \circ a) \circ a) \circ a \,=\, a \,+\, 3$ This is similar to addition: Neutral element: $^^{0 \,=\, \frac{1}{\infty} \,=\ \div \infty}$ $\,\,\,\div\infty \,=\, a \,.\, 0$ $\,\,\,\div\infty + a \,=\, a \,.\, 1$ $\,\,(\div\infty + a) + a \,=\, a \,.\, 2$ $((\div\infty + a) + a) + a \,=\, a \,.\, 3$ Also is similar to product: Neutral element: $^^{1 \,=\, n^{\frac{1}{\infty}} \,=\ \sqrt[\infty]{n}}$ $\,\,\,\,\,\sqrt[\infty]{n} \,=\, a^0$ $\,\,\,\,\,\sqrt[\infty]{n} \,.\, a \,=\, a^1$ $\,\,(\sqrt[\infty]{n} \,.\, a) \,.\, a \,=\, a^2$ $((\sqrt[\infty]{n} \,.\, a) \,.\, a) \,.\, a \,=\, a^3$ And is similar to exponentiation Neutral element: $^^{1 \,=\, ?_{(\infty,n,b)}$ where I conjecture that "?" is the inverse function of tetration, and is not slog. $\,\,\,\,\,\,\,\,\sqrt[\infty]{n} \,=\, ^0a$ $\,\,\,\,\,a^{\sqrt[\infty]{n}} \,=\, ^1a$ $\,\,a^{a^{\sqrt[\infty]{n}}}\,=\, ^2a$ $a^{a^{a^{\sqrt[\infty]{n}}}} \,=\, ^3a$ Note that the neutral elements are all related with the inverse of the higher ranked operation. I think that it is a very important clue. $-\infty= 0-\infty$ $^^{0 \,=\, \frac{1}{\infty} \,=\ \div \infty}$ $^^{1 \,=\, n^{\frac{1}{\infty}} \,=\ \sqrt[\infty]{n}}$ But why I choose $^{-\infty}$ as the neutral element of zeration? -Because it is $^{-\infty= 0-\infty}$ -Because $^{-\infty\,\circ\, -\infty \,=\, -\infty \,+\, 1 \,=\, -\infty}$ -Because this sequence: $ln(a^1)=ln(a) . 1$ $ln(a.1)=ln(a) + 0$ $ln(a+0)=ln(a) \circ [-\infty=ln(0)]$ I conjecture that zeration has a periodic component, so it can just add 1 no matter how high are his variables, and also ln(a+b) could be equal to ln(a) ° ln(b) ln(a+b)=ln(a)+ln(1+b/a) if a>b => 0 < ln(1+b/a) < ln(2) If a=b => ln(1+b/a) < ln(2) this is suspiciously like zeration, adding a small number to the larger number, or adding 2 if a=b « Next Oldest | Next Newest »

 Messages In This Thread Zeration - by GFR - 02/14/2008, 06:38 PM RE: Zeration - by Ivars - 02/14/2008, 08:10 PM RE: Zeration - by GFR - 02/14/2008, 10:41 PM RE: Zeration - by mathamateur - 07/30/2009, 06:31 AM RE: Zeration - by Ivars - 02/21/2008, 07:22 PM RE: Zeration - by quickfur - 02/21/2008, 09:34 PM RE: Zeration - by bo198214 - 02/21/2008, 10:18 PM RE: Zeration - by bo198214 - 02/21/2008, 10:25 PM RE: Zeration - by quickfur - 02/21/2008, 11:04 PM RE: Zeration - by quickfur - 02/21/2008, 11:12 PM RE: Zeration - by KAR - 02/21/2008, 11:04 PM RE: Zeration - by quickfur - 02/21/2008, 11:52 PM RE: Zeration - by GFR - 02/24/2008, 12:39 AM RE: Zeration - by Ivars - 02/24/2008, 02:50 PM RE: Zeration - by marraco - 03/20/2015, 09:59 PM RE: Zeration - by bo198214 - 02/24/2008, 11:02 AM RE: Zeration - by GFR - 03/19/2008, 12:40 PM Zeration - My Research / Investigation - by James Knight - 03/25/2008, 08:28 AM RE: Zeration - My Research / Investigation - by bo198214 - 03/25/2008, 09:09 AM More on Zeration - by James Knight - 03/25/2008, 03:44 PM Exponential Laws - New Zeration Law - by James Knight - 03/25/2008, 07:48 PM Delta Numbers As HyperReals - by James Knight - 03/26/2008, 12:50 AM RE: Delta Numbers As HyperReals - by Ivars - 03/26/2008, 12:15 PM RE: Zeration - by GFR - 03/26/2008, 12:22 AM RE: Zeration - by GFR - 04/05/2008, 08:58 PM RE: Zeration - by Igor M - 01/14/2009, 04:04 PM RE: Zeration - by bo198214 - 01/20/2009, 09:59 PM RE: Zeration - by 73939 - 07/05/2010, 12:00 AM RE: Zeration - by bo198214 - 07/05/2010, 07:37 AM RE: Zeration - by brangelito - 07/20/2010, 05:51 PM RE: Zeration - by bo198214 - 07/21/2010, 02:58 AM RE: Zeration - by JmsNxn - 11/09/2011, 01:40 AM RE: Zeration - by quickfur - 11/09/2011, 04:15 AM RE: Zeration - by JmsNxn - 11/10/2011, 01:20 AM RE: Zeration - by quickfur - 11/10/2011, 02:09 AM RE: Zeration - by marraco - 03/20/2015, 09:44 AM RE: Zeration - by marraco - 03/20/2015, 10:41 PM RE: Zeration - by marraco - 03/21/2015, 12:35 AM RE: Zeration - by marraco - 03/21/2015, 01:44 AM RE: Zeration - by marraco - 03/21/2015, 04:10 AM RE: Zeration - by MphLee - 03/21/2015, 11:53 AM RE: Zeration - by marraco - 03/23/2015, 07:58 AM RE: Zeration - by tommy1729 - 03/21/2015, 11:11 PM RE: Zeration - by marraco - 03/23/2015, 08:05 AM RE: Zeration - by marraco - 03/24/2015, 11:29 AM RE: Zeration - by MphLee - 03/23/2015, 09:00 AM RE: Zeration - by marraco - 03/23/2015, 01:39 PM RE: Zeration - by MphLee - 03/23/2015, 02:31 PM RE: Zeration - by Stanislav - 05/28/2015, 11:12 PM RE: Zeration - by marraco - 05/29/2015, 01:33 AM RE: Zeration - by Stanislav - 05/29/2015, 09:06 PM RE: Zeration - by MphLee - 06/03/2015, 01:40 PM RE: Zeration - by Stanislav - 06/04/2015, 06:44 AM RE: Zeration - by marraco - 06/04/2015, 08:44 PM RE: Zeration - by MphLee - 06/05/2015, 09:10 PM RE: Zeration - by Stanislav - 09/09/2015, 10:04 PM RE: Zeration - by Stanislav - 10/31/2016, 02:57 PM

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