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No, this will not surpass the supersupersuper...........supersuper w/super super's BEAF at the very least, the linear arrays. \(a\)\(l\)\(t\) 07:42, April 28, 2013 (UTC)

Conventional sign for rest[]

This is #, used by Bowers. @ was used later when Saibian made his Hyper-E notation and # conflicted with hyperion-separator mark. Ikosarakt1 (talk ^ contribs) 12:12, July 14, 2013 (UTC)

Growth rate[]

Growth rate of the question mark is \(n?=n![1(1)[_{<1(n)2>⁅n⁆}1]]=\psi(\psi_{I_\omega}(0))\), and the limit of HAN is \(n![1(1)\alpha\mapsto[_{<1(1)2>⁅\alpha⁆}1]]\), which is approximately \(\psi(\psi_{I_I}(0))\). So please add it to the function label. hyp$hyp?cos&cos (talk) 02:03, November 8, 2013 (UTC)

Are we sure? FB100Ztalkcontribs 07:26, November 8, 2013 (UTC)


Dammit who keeps reverting my "bracketed operator" edits? THEY ARE NOT WRONG


n!m = n{m}n-1{m}n-2{m}n-3{m}...{m}3{m}2{m}1


Also, would be better if n!!m = n!n!n!........!n m times


Antares 3^^^3 12:45, February 27, 2015 (UTC)

Could there possibly be an article to elaborate a little more in-depth on the subtleties and complex rules of this function sometime? I know that his original site included all the rules on it, but it is still a little hard to read at the present. I think it would be very helpful. 70.114.180.72 05:44, December 19, 2015 (UTC)

Yes, I agree. Reading these rules, it's not clear at all to me that 3![1,[1,3,2],4]=3![1,[[1,1,2],2,2],4] (from the rules, that is). Maybe called Googology Noob (talk) 06:18, January 19, 2016 (UTC)
It's more clear in his blog posts and web page. For 3![1,[1,3,2],4], you go to the first non-1 entry, which is the 3 in [1,3,2]. Since the 3 is preceded by "1,", you use the following rule: decrement the 3 to 2, then replace the previous 1 by the the array at that level with the 3 replaced by 1, which would be [1,1,2]. So [1,3,2] is replaced by [[1,1,2],2,2]. Deedlit11 (talk) 16:20, January 20, 2016 (UTC)

Introduction to HAN?[]

Somebody should create an "Introduction to HAN" page, (If it doesn't exist already.)

This might be me being a noob, but the current HAN page is as clear as mud, so an Introduction page for HAN (Like the Introduction to BEAF page, or the Introduction to Extensible-E page.) would be SUPER useful to me, and i'm sure many others.

2601:142:2:EC49:5144:D1E7:12C6:B1DF 14:22, August 4, 2018 (UTC)

There needs to be an explicit confirmation of HAN's growth rate[]

The rate given on the wiki's function list is \(f_{\psi(I_\omega)}\), whatever that means, and without any specification of \(\psi\)! On his blog, Hollom says he believes this system reaches TFB, not whatever's listed on the wiki. Most importantly, I haven't seen anybody confirm any growth rate whatsoever, let alone on this page. Could somebody please check this out? QuasarBooster (talk) 06:44, March 1, 2020 (UTC)

Could you tell me which list you are referring to? I guess that the growth rate is conjectured by hyp cos above, but has no actual formal meaning, because results of that level with an unspecified psi is meaningless. It is good to remove the result.
p-adic 07:50, March 1, 2020 (UTC)
It's on the full function list here https://googology.wikia.org/wiki/List_of_functions#ZFC_set_theory near the lower part of the ZFC section. Ideally, we'd be able to replace it with a growth rate that is actually confirmed. QuasarBooster (talk) 14:48, March 1, 2020 (UTC)
Thank you! I reordered it.
p-adic 23:01, March 1, 2020 (UTC)

The definition of the hyperfactorial n!m[]

n!m is n[m]((n−1)[m]((n-2)[m]...[m](3[m](2[m]1))...)), where [m] is the m-ation (hyper-m), e.g. [5] is pentation, [6] is hexation, thus, n!2 is the classic factorial n!, and n!3 is the "exponential factorial", n!m is the m-ation (not the (m+2)-ation) for 1 to n, see [1], also, n!m is also written as n[m]!

m\n 0 1 2 3 4 5 6
1 0 1 3 6 10 15 21
2 1 1 2 6 24 120 720
3 1 1 2 9 262144 5262144 65262144
4 1 1 2 27 4 [4] 27 = 4^4^4^...^4^4^4 with 27 4s
5 1 1 2 7625597484987 4 [5] 7625597484987

Xayahrainie43 (talk) 05:31, May 4, 2020 (UTC)

Do I evaluate 3![[4[31]]] as 3![[2[4[31]]]] or 3![[4[2[31]]]]?[]

Ham numbers (talk) 23:55, 15 December 2023 (UTC)

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