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 Zeration = inconsistant ? MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 10/04/2014, 12:58 PM (10/04/2014, 11:24 AM)MphLee Wrote: the solution of the equation $x \odot_e^{a}x=b$ should be, as you say $\exp^{\circ a}( 2 ln^{\circ a} (x) ) = b$ $x={\exp}^{\circ a}(\frac{ln^{\circ a}(b)}{2})$ I guess is possible to do more here... I'll try to find a forumula only involving homomorphic operators defined via exponential... I looked at it better and is easy to write. The solution of the equation $x \odot_e^{a}x=b$ is $x=b\oslash_e^{1+a} {\exp}^{\circ a}(2)$ where $\oslash_e^{1+a}$ is the inverse operation of $\odot_e^{a+1}$ so we should have $x \odot_e^{a}x=x\odot_e^{a+1}{\exp}^{\circ a}(2)$ Anyways i'm not 100% sure. I have to chek it with calm. (10/04/2014, 12:16 PM)tommy1729 Wrote: I already made the choice : a [0] b = max(a,b) + 1 + kroneckerdelta(a,b) regards tommy1729 Ok i get it... Well first of all $(-1)$-ation should have a non-empty intersection with RR-Zeration RR-Zeration: $a [0]_{RR} b = max(a,b) + 1 + \delta_{ab}$ $[0]_{RR} \cap [-1]\neq \emptyset$ Their intersection has to contain a segment of the trivial zeration (the successor of the second argument) because in that segment $(-1)$-ation is the subfunction of RR-Zeration. Anyways I think that if we chose RR Zeration $(-1)$-ation its gonna be a multivalued oepration (see Hyperstructures theory and multimaps and this Brief introduction by Viro, comment by Mphlee) Why? Because its translations are not invertible functions. Anyways I guess that using the Litinov-Maslov's Limit Process we could find a formula that show to us the real shape/behaviour of the set $[-1]$. MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

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