Multi Dimensional PVN MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 06/20/2013, 11:41 AM   MultiDimPVN.pdf (Size: 525.25 KB / Downloads: 586) Place Value Notation is the way we usually think about the natural numbers. It is possible to say a few things about multi dimensional Place Value Notation. I use the term "ordertype" and "folding pattern" from my previous papers (see "Nept and Nopt Structures") tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 06/22/2013, 08:46 PM With respect , but I fail to see how this relates to tetration. MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 06/23/2013, 12:40 AM (06/22/2013, 08:46 PM)tommy1729 Wrote: With respect , but I fail to see how this relates to tetration. in the section extending place value notation into pure noptiles there is a formula relating brace notation to 10^^9 (10 tetrated to 9) MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 06/25/2013, 12:49 AM   mdpextra.pdf (Size: 117.51 KB / Downloads: 257) There is an obvious relationship between hyper4 and iterated brace notation with standard positional notation. The pdf has some examples that show how tetration (with positive integers) is related to SPN using the brace notation. MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 07/07/2013, 01:02 PM thank goodness that you can check what should be obvious common sense on Wolfram Alpha http://www.wolframalpha.com/input/?i=googol interesting to contemplate about MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 07/07/2013, 01:32 PM it is interesting to see what a googol looks like in base 2 wolfram alpha gives this information what about googolplex ? is that too complex to specify in base 2 ? Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 07/08/2013, 10:23 PM (This post was last modified: 07/08/2013, 10:25 PM by Gottfried.) (07/07/2013, 01:32 PM)MikeSmith Wrote: it is interesting to see what a googol looks like in base 2 wolfram alpha gives this information what about googolplex ? is that too complex to specify in base 2 ? Hmm, did you know that in 2007 I proposed a summation for the series $a_{10}(2) = 2 - 10^2 + \text{googol} - \text{googolplex} + 10^{\text{googolplex}} - ... + ... \approx 0.336339355$ If you start meditating about this, well, I don't know what will happen... :-) Gottfried Gottfried Helms, Kassel sheldonison Long Time Fellow Posts: 626 Threads: 22 Joined: Oct 2008 07/09/2013, 09:40 PM (This post was last modified: 07/09/2013, 09:41 PM by sheldonison.) (07/08/2013, 10:23 PM)Gottfried Wrote: .... Hmm, did you know that in 2007 I proposed a summation for the series $a_{10}(2) = 2 - 10^2 + \text{googol} - \text{googolplex} + 10^{\text{googolplex}} - ... + ... \approx 0.336339355$ .... GottfriedHow do you calculate the sum of this super-exponentially growing alternating series? Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 07/10/2013, 01:24 AM (07/09/2013, 09:40 PM)sheldonison Wrote: (07/08/2013, 10:23 PM)Gottfried Wrote: .... Hmm, did you know that in 2007 I proposed a summation for the series $a_{10}(2) = 2 - 10^2 + \text{googol} - \text{googolplex} + 10^{\text{googolplex}} - ... + ... \approx 0.336339355$ .... GottfriedHow do you calculate the sum of this super-exponentially growing alternating series?It is a conjecture because some convergence in the required matrix-formula was only observed for truncated matrices but I could not prove them. Here is the initial article of 2007 (which is much amateurish since I was just entering the field of tetration) http://go.helms-net.de/math/tetdocs/10_4...rticle.pdf ; later I did a conversation in sci.math.research to improve the plausibility of the results, I've collected that discussion at http://go.helms-net.de/math/tetdocs/Iter...tion_1.htm . Gottfried Gottfried Helms, Kassel MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 01/07/2014, 03:49 AM This extra info follows on from the previous document. While the formulae aren’t so pretty to look at or check for accuracy, the result at the end of this additional document shows that the philospophical notion of regular type dimensional PVN does have an associated numerical expression result for ordertype[5]. Beyond this, the formulae expression would clearly be too cumbersome to bother with. However, the ordertype[5] result is interesting and quite understandable. Finally, the generalised expression is given for ordertype[5]. The prerequisites for understanding are contained in the previous documents about multi type dimensional PVN. Unfortunately, in the conversion from word document to pdf document some of the braces are no longer visible. Attached Files   mdimextrainfo.pdf (Size: 425.06 KB / Downloads: 221) « Next Oldest | Next Newest »