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 Zeration JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 11/09/2011, 01:40 AM (This post was last modified: 11/09/2011, 01:47 AM by JmsNxn.) This is a rather disturbing flaw that I've come across with zeration that rather surprises me the authors didn't consider. By the Ackermann function: $\text{(I)}\,\,a\,\,\bigtriangleup_\sigma\,\,(a\,\,\bigtriangleup_{\sigma +1 }\,\,b) = a\,\,\bigtriangleup_{\sigma + 1}\,\,b+1$ which is the core of how the function is defined. I'm gonna put it right out there that zeration DOES NOT satisfy this property. by definition: $a\,\,\circ\,\,b = max(a,b) + 1$ or $a\,\,\circ\,\,b = a + 2 = b + 2\,\,\text{if a = b}$ Take the obvious example, a > 0: $a\,\,\circ\,\,(a + (-1)) = max(a, a-1) + 1 = a + 1$ however, by Ackermann's law (I): $a\,\,\circ\,\,(a + (-1)) = a + (-1) + 1 = a$ Did anybody else notice this? How could they over look such a fatal flaw? I mean it took me fifteen minutes of research to see this? It can actually be extended generally to all negative numbers $k \in \mathbb{R}\,\,;\,\,k<0$ $a\,\,\circ\,\,(a - k) = a + 1$ however by (I) we know it must be $a\,\,\circ\,\,(a - k) = a - k + 1$ Clearly Zeration is not the operator below addition in the Ackermann function. « 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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