MultiDimPVN.pdf (Size: 525.25 KB / Downloads: 623)
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")

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.

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 ?

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

If you start meditating about this, well, I don't know what will happen... :-)

(07/08/2013, 10:23 PM)Gottfried Wrote: ....
Hmm, did you know that in 2007 I proposed a summation for the series

....
Gottfried

How 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 .

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.