Talk:TREE sequence/Archive 1

Can we get the original source for this instead of Wikipedia? FB100Z &bull; talk &bull; contribs 02:18, September 13, 2012 (UTC)

Perhaps it comes from "Enormous Integers In Real Life". Ikosarakt1 (talk) 15:20, October 6, 2012 (UTC)

Anyways, what is the TREE sequence anyway? The article doesn't explain it. FB100Z &bull; talk &bull; contribs 03:54, October 20, 2012 (UTC)

See "chapter 11" for formal definition. As for values, see: http://www.cs.nyu.edu/pipermail/fom/2006-March/010279.html Ikosarakt1 (talk) 08:00, October 20, 2012 (UTC)

I guess that TREE(3) is between humongulus and golapulus. --Cloudy176 (talk) 13:57, October 24, 2012 (UTC)

In fact: TREE(3) larger than fГ(3) = {3,3,1,2} & 3, which is larger than humongulus = {10,10,100} & 10. Ikosarakt1 (talk) 18:57, October 25, 2012 (UTC)

Hmm, my reasoning leads me to believe fГ 0 (n) is about n & n & n... & n with n n's. This would make TREE(3) much larger than golapulus Deedlit11 (talk) 16:19, November 16, 2012 (UTC)

Golapulus is already ~ {10,100 [1 [1 --| 1 [2] 2] 2} (there: --| is negation sign), but TREE(n) growth is about {3,n [1 [1 --| n] 2] 2} (small Veblen ordinal) Ikosarakt1 (talk) 09:07, November 17, 2012 (UTC)

I assume you are getting those correspondences from Bird's "Bowers Named Numbers", is that correct?? I'm not sure I agree with all the findings.? As I explained in my blog comment, I think Gamma_0 should correspond to n & n & n ... & n with n n's.? So the small Veblen ordinal will certainly be greater than that.

I should point out that the small Veblen ordinal is merely a lower bound for the growth rate of TREE(n). As far as I know, no good upper bound has been found.Deedlit11 (talk) 00:57, November 23, 2012 (UTC)

In this case, need to reconsider the comparison of TREE with array notations. Ikosarakt1 (talk) 12:16, November 23, 2012 (UTC)

After more detailed research on fast-growing hierarchy I am sure that TREE(3) far larger than meameamealokkapoowa oompa (see blog comment). Ikosarakt1 (talk) 15:33, November 24, 2012 (UTC)

TREE(3) made into a game --Cloudy176 (talk) 10:25, December 26, 2012 (UTC)

If your calculations are all correct, then (say) TREE(1,000) will certainly be larger than meameamealokkapoowa oompa. However, I still have doubts that TREE(3) is larger than meameamealokkapoowa oompa. --I want more clouds! 05:02, December 31, 2012 (UTC)

\(f_{\psi(\Omega^\omega)}\)(n)
Is \(\psi(\Omega^\omega)\) is the same ordinal as \(\vartheta(\Omega^\omega)\)? Ikosarakt1 (talk) 10:45, February 23, 2013 (UTC)


 * No, they're different. \(\psi(\Omega^\omega)=\vartheta(\omega)\), while \(\vartheta(\Omega^\omega)=\psi(\Omega^{\Omega^\omega})\). See . I want more clouds! 11:29, February 23, 2013 (UTC)
 * Hmm, ordinal collapsing function definitions may vary by authors. Maybe they are equal, or may not... I want more clouds! 11:31, February 23, 2013 (UTC)

Ordered vs unordered siblings
I wanted to point out that there are two definitions of homeomorphic embeddability with rooted trees: the one with ordered siblings, and other one with unordered. On this site and on Goucher's blog we are with no doubt using unordered version, for which trees ([]) and ([]) are equivalent. But, if I'm not mistaken, even Kruskal himself used ordered version. This is because he interpreted trees as set of integer strings closed under prefixes. Friedman certainly used this version, because otherwise n(4) argument fails. Here is same story. Ordered siblings make much difference in tree(n) function too. Let utree(n) mean unordered version and otree(n) ordered version. It should be clear that \(utree(n)\leq otree(n)\). I found out that \(utree(2)=otree(2)=5\), \(utree(3)\geq 2^{17}+8\) and \(otree(3)\geq 2\uparrow ^6 3\), so difference quickly becomes significant. Which version you think we should use? Friedman's one, or Goucher's one? LittlePeng9 (talk) 12:43, February 23, 2013 (UTC)

Bird's hierarchy
When Chris Bird writes that"[X] has level \(\alpha\)", he doesn't means that \(f_{\alpha}(n)\) is about {n,n [X] 2}. Rather, he creates his own hierarchy of separators, if you look closer. Ikosarakt1 (talk) 10:04, February 26, 2013 (UTC)


 * But that is irrelevant to the information you removed. That was the result Chris Bird has shown in the paper. I don't think it should be removed. I want more clouds! 10:55, February 26, 2013 (UTC)

Where Bird was stated that? I opened "Beyond Nested Arrays II" document, page 10, but Bird doesn't says there about TREE(3) strictly. Ikosarakt1 (talk) 11:10, February 26, 2013 (UTC)

you seem older version of his work. in the new version of 13.02.2013 on page 10.