• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Zeration = inconsistant ? GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 10/04/2014, 10:19 AM (This post was last modified: 10/04/2014, 10:22 AM by GFR.) (10/01/2014, 08:40 AM)tommy1729 Wrote: ........ To understand tetration you need to understand +,*,^ at least. To understand ^ you need to understand *. To understand * you need to understand +. Defining and understanding a hyperoperator seems to require the lower hyperoperators. But with zeration that is A PROBLEM. ..... ..... properties like distributive require use of a lower hyperoperator : a * (b+c) = a*b + a*c. .... Zeration seems to lack properties and therefore consistancy. regards tommy1729 As a matter of fact, if you apply these principles, you would indeed discover a problem with ... 'Addition', because: "To understand + you (would) need to understand o!". In fact, we should have (sorry for 'o' and, please, forget 'some' useless brackets): a * a = a ^ 2; a * (a * a) = a ^ 3 a + a = a * 2; a + (a + a) = a * 3 a o a = a + 2; a o (a o a) = a + 3. And, moreover, as we have seen: a + (b o c) = (a + b) o (a + c), i.e. the 'descending' distributivity seems to hold! And ... to gain consistency! And, don't forget: 2o2 = 2+2 = 2*2 = 2^2 = 2#2 = .... 2[s]2 = 4. The 'Magic Four' relation! Thank you for your interest. Best regards. GFR « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Zeration GFR 80 171,559 10/31/2016, 02:57 PM Last Post: Stanislav Zeration reconsidered using plusation. tommy1729 1 5,426 10/23/2015, 03:39 PM Last Post: MphLee Is this close to zeration ? tommy1729 0 3,687 03/30/2015, 11:34 PM Last Post: tommy1729 [2015] 4th Zeration from base change pentation tommy1729 5 11,135 03/29/2015, 05:47 PM Last Post: tommy1729 [2015] New zeration and matrix log ? tommy1729 1 5,770 03/24/2015, 07:07 AM Last Post: marraco [2014] Inconsistant equation ? tommy1729 0 3,186 07/27/2014, 02:38 PM Last Post: tommy1729 base change inconsistant ? tommy1729 2 5,581 11/26/2012, 08:13 AM Last Post: Nasser

Users browsing this thread: 2 Guest(s)