Bubby3 showed that (*,b) is the diagonalizer of (*,b-1). It can also be said as below;
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Though I'm thinking of a changing the method of the bad root (=the rightmost node of the bad part, =D-value of Bubby3's) decision to fix Bashcu Matrix System version BM1 as like 'how to fix it' section of Bubby3's post, I found another approach.
- Write all rows in hydra notation.
- Mark all ancestors of the rightmost nodes of each rows.
- The rightmost node which is the ancestors in the all rows (=concestor) is decided as the bad root (=D-value).
With this approach, (0,0)(1,1)(2,2)(3,3)(4,1)(3,2)(4,2)(5,2) takes (0,0) for the (0,0) instead of (1,1). (1,1) isn't the ancestor of the B in the figure below in the second row. I think this is better than Bubby3's which can have mistake of the selection of the ancestors by erasing branch for the upper ro…
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Here is the hydra notations of the Pair sequence system Googleaarex analyzed.
- Complete full size PNG: http://www.ukaibutton.com/hydraviewer/aarex_pair.png
I made a Hydra Viewer program and I used it to draw the hydra notation. (source code at github)
The hydra notation of the Pair sequence system is based on the Bashicu's explanation at SlideShare .
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Very beautiful. I hope they can be help for your analysis and your proof.
Here is new SNS for talking about Googology!
Googoldon is a twitter-like SNS in which Mathjax is available. I want to make this site global, so any languages will do in this site. Any type of discussions, ideas, questions, monologue will do. Please try it!Read more >
Hi, my name is koteitan. Here is a "Googol Maps", it is a poster-size map I made for you to get a picture of the Googology activities.
Fullsize jpg : http://www.ukaibutton.com/googology/GoogolMaps_En.jpg
On this map, the time goes on from top to bottom and the bigger numbers are shown on the right side. The kinds of the notations, the number-generating system or methodologies are categolized and differently colored. The arrows indicate the evolution of each number or functions. The arrows with dashed line shows 'inspired' connections of the idea of them.
After making this map, I was really surprised to find that there was so many variations of the large numbers, and their rapid evolutions!
This map was made only by myself now, so that it may i…
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