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Googology Wiki

Hello, welcome to the wiki! FB100Ztalkcontribs 17:31, March 26, 2013 (UTC)


Can you please show me your current notations on the large numbers? Ikosarakt1 (talk ^ contribs) 19:27, March 26, 2013 (UTC)

We'd love to see your stuff! Factorials have not seen much serious extension since the Torian. FB100Ztalkcontribs 20:25, March 26, 2013 (UTC)
Check my blog post about factorials. Ikosarakt1 (talk ^ contribs) 21:02, March 26, 2013 (UTC)

Largest number... Gigoombaverse... It is the largest number, larger than meameamealokkapoowa oompa. Think you can coin the bigger number then the gigoombaverse? good luck (but not bad luck).
\(a\)\(l\)\(t\) 11:58, March 29, 2013 (UTC)

Gigoombaverse sucks. You know what's better? Croutonillion. FB100Ztalkcontribs 16:37, April 26, 2013 (UTC)

Of course, it gets larger over time. Pi.jayk (talk) 20:37, June 1, 2018 (UTC)

You know what’s even better than Croutonillion? Sam’s number. DrCocktor (talk) 16:55, July 16, 2018 (UTC)


What is definition of kilohugexul number? It appears in definition of superior kilohugexul, but its definition doesn't. Also, based on this, how does sequence for grand superior hugexul continue? LittlePeng9 (talk) 15:38, April 26, 2013 (UTC)

According to this page, Kilohugexul = Hugexul![1,...,1,2] (with 200 entries, including the last 2). I want more clouds! 15:52, April 26, 2013 (UTC)
Thanks, I haven't seen that page. LittlePeng9 (talk) 15:59, April 26, 2013 (UTC)

DrCeasium, next time use the source mode, we dont want to keep cleaning up the spans/. Thanks. \(a\)\(l\)\(t\) 03:08, April 28, 2013 (UTC)


Do you live in UK? \(a\)\(l\)\(t\) 09:06, May 8, 2013 (UTC)

Yes, he does. It says so on the Googology Wiki page for Lawrence Hollom. Pi.jayk (talk) 20:47, June 1, 2018 (UTC)


Is BIGG larger than meameamealokkapoowa oompa? \(a\)\(l\)\(t\) 09:38, May 25, 2013 (UTC)

I currently think that my numbers overtake the meameamealokkapoowa oompa somewhere around Hugebixul, but i'm not sure. If they don't overtake it there, then i'm pretty certain that they will definitely have done so by the BIGG, so in answer to your question, probably yes.DrCeasium (talk) 09:45, May 25, 2013 (UTC)
Well done, if yes... You take how much effort? \(a\)\(l\)\(t\) 09:55, May 25, 2013 (UTC)

We want back the ½, maybe we shall call it BIGGG. Jiawhien (talk) 11:02, June 9, 2013 (UTC)

BIGGG can stand for Bewilderingly Incomprehensibly Great Ginormous Googolism

BIGGGG can stand for Bewilderingly Incomprehensibly Grand Great Ginormous Googolism

BIGGGGG + glorious

BIGGGGGG + gratuitous

BIGGGGGGG + gigantic

HUGE can stand for Horrible Unspeakable Ginormous Expression Wythagoras (talk) 18:42, June 10, 2013 (UTC)

Using these layman's words isn't a good idea, we can't name, for example, BIGGG...GGG (with Graham's number G's). Ikosarakt1 (talk ^ contribs) 18:52, June 10, 2013 (UTC)

Is BIGG larger than Rayos number? Pi.jayk (talk) 20:55, June 1, 2018 (UTC)


An extremely small number in your lota function is lota((1/lota(BIGG))). And Do you think that it is bigger than Xi? Jiawhien (talk) 10:22, May 31, 2013 (UTC)

The Iota function is sort of cheating really, because it just calls every other function in existence (excluding itself), so yes it will be bigger than everything else, but I don't really like it and it's not a serious competitor for the uncomputables.DrCeasium (talk) 10:30, May 31, 2013 (UTC)

Numbers List on your site

On your full number list is a mistake:

Hugexul = 200![200(1)200], but

Hugebixul = 200![200(1)200]

I think that Hugebixul should have an additional (1)200

Wythagoras (talk) 17:39, June 4, 2013 (UTC)

fixed it. Thanks for pointing it out.DrCeasium (talk) 16:32, June 6, 2013 (UTC)

Iota function

I like concept of your Iota function, but the mayor flaw in it is point where you say "with the least powerful nearest the n". There is no well agreed method of saying which function is more powerful. For example, take functions \(f(x)=x\text{ and }g(x)=x+\varepsilon \text{sin}x\) for some small \(\varepsilon\), so that g(x) is increasing. g(x) will oscillate between being larger and smaller than f(x), so it is hard to say which function is more powerful. LittlePeng9 (talk) 17:09, June 5, 2013 (UTC)


I'm trying to understand your notation and I'm drowning in @ signs! Can you explain to me how the w/ operator and multidimensional arrays work?

(I also feel that the @ sign is really a poor choice — not your fault, just a funky convention. Instead of using \(@_1,@_2,@_3,\ldots\) I would recommend using geometrical shapes: \(\bullet,\circ,\diamond,\ldots\)) FB100Ztalkcontribs 21:33, June 5, 2013 (UTC)

We really need to agree on a definite 'rest of array' symbol. I like your idea of the shapes, and it does seem to make it a lot easier to read. At some point i'll re-write the definitions using these symbols.DrCeasium (talk) 16:26, June 6, 2013 (UTC)
The "@" is the part of the expression. Jiawhien (talk) 11:03, June 9, 2013 (UTC)


You are one year older than me. Jiawhien (talk) 05:02, June 10, 2013 (UTC)

I think that you're 13 or so. Ikosarakt1 (talk ^ contribs) 18:50, June 10, 2013 (UTC)

Hey, DrCeasium was born same year as me! LittlePeng9 (talk) 19:57, June 10, 2013 (UTC)

Pffft. Kids these days. FB100Ztalkcontribs 20:26, June 10, 2013 (UTC)

@FB100Z, No. 01:03, June 11, 2013 (UTC)
@Ikosarakt1, Yes. 01:03, June 11, 2013 (UTC)
Neither of us were asking questions :/ FB100Ztalkcontribs 02:43, June 11, 2013 (UTC)
I am late 13. \(a\)\(l\)\(t\) 03:20, June 11, 2013 (UTC)

Wow, so many young people!!! (I'm 18 btw) Tomtom2357 (talk) 17:05, July 27, 2015 (UTC)

Destruxul vs. Destrucxul

How it must be spelled correctly? Ikosarakt1 (talk ^ contribs) 17:40, June 11, 2013 (UTC)

Destruxul DrCeasium (talk) 19:21, June 11, 2013 (UTC)

Rule R2

How to start to solve 3![1(1)3], under the rule R2? 3![1(1)3] can expand to either 3![1(1)2]/w(0)[1(1)2]/w(0)[1(1)2] (there are 3 [1(1)2]'s) or 3![1(1)2]/w(0)[1(1)2]/w(0)[1(1)2]/w(0)[1(1)2] (there are 3 /w(0)'s). I know there is no big difference in terms of growth rates, but still: what is correct? Ikosarakt1 (talk ^ contribs) 16:05, June 21, 2013 (UTC)

3 [1(1)2]'s DrCeasium (talk) 20:15, June 21, 2013 (UTC)

(Supposing that first variant was correct)

Also, even if we take the only simplest examples in dimensional arrays: 3![1(1)2] = 3![1(1)1]/w(0)[1(1)1]/w(0)[1(1)1] = 3![1],[1],[1] (which is definitely, incorrect).

There is another question: what means ® on your website? No definition given for it. Ikosarakt1 (talk ^ contribs) 16:12, June 21, 2013 (UTC)

it was defined at the top along with Db, Dw and 0m. It means any amount of '['s DrCeasium (talk) 20:15, June 21, 2013 (UTC)

Question about the w/ chain: How to solve 3![1]w/[1,2,2]w/[1,3] ? Is it 3![1]w/[[1]w/[1,1,2]w/[1,3],1,2]w/[1,3], 3![1]w/[[1]w/[1,1,2],1,2]w/[1,3], 3![1]w/[[1,1,2]w/[1,3],1,2]w/[1,3] or 3![1]w/[[1,1,2],1,2]w/[1,3] ? {hyp<hyp··cos>cos} (talk) 01:24, October 19, 2013 (UTC)

3^^^3 is tritri

3^^^3 is officially called tritri, not that you wrote here. Ikosarakt1 (talk ^ contribs) 09:39, June 23, 2013 (UTC)

It can also be written as {3,3,3} in BEAF. Pi.jayk (talk) 23:03, June 4, 2018 (UTC)

HAN can be much stronger

I have discovered a much better version of dimensional HAN. It will reach \(\vartheta(\Omega_2)\) and there is only a small change needed: if you evaluate a subarray in a array, for example [1(1)1(1)[1,2]], it must be evaluated to [1(1)1(1)[1,2]] [1(1)1(1)[1(1)1(1)[1,1]]] or something that fits in your rules, but copies the whole array.

Also, if you don't make the change, I'm afraid that type n brackets won't reach the TBF. Wythagoras (talk) 09:24, July 4, 2013 (UTC)

I'm not really sure I understand your example: it seems that the second expression is far larger than the first. Also, the dimensional array's power should have very little influence on the power of the bracket types. Why do you think that they won't reach the TFB? (blog post about it here) DrCeasium (talk) 16:38, July 4, 2013 (UTC)

Sorry. I did stupid. Wythagoras (talk) 12:14, July 5, 2013 (UTC)

FB100Z's promise

Did you really meet him in the real world? Ikosarakt1 (talk ^ contribs) 17:48, July 4, 2013 (UTC)

No. DrCeasium (talk) 18:26, July 4, 2013 (UTC)

Nucleaxul numbers

is Nucleabixul \([[_{[[_{200}200]]}200]]\) or \([[_{[_{200}200]}200]]\)? your site shows the old definition. About your site, there are many things incorrect. In the article about BEAF are some comparisons incorrect. Also, your smallest number bigger then meameamealokkapoowa oompa is extremexul, not hugebixul. Wythagoras (talk) 15:47, July 31, 2013 (UTC)

I know, there are plenty of mistakes. I've been putting off sorting them out for some time now. I'll see if I can fix them soon. As for the numbers, I haven't actually done anything with them for ages. I think the nucleabixul should be the second, more powerful definition. DrCeasium (talk) 12:12, August 1, 2013 (UTC)


So I accidentally found your upcoming EFAN page (sorry about that :P). All I can say is: THAT. WAS. AMAZING. King2218 (talk) 08:54, May 20, 2014 (UTC)

I found it too. 0_____e you'! 09:35, May 20, 2014 (UTC)
I found it too.
I don't really get it, but it looks neat. LittlePeng9 (talk) 14:07, May 20, 2014 (UTC)
Well, Hollom's target was initially "beating" meameamealokkapoowa oompa, about which he thinks as the largest computably defined number so far, but it turned out to be just a scary word. Let's look who in our community will beat Loader's number and establish the record first. Ikosarakt1 (talk ^ contribs) 15:17, May 20, 2014 (UTC)
It's been sitting there for a couple of months now. I'm currently busy with exams, but in a few weeks, when they're over, I should be able to come back and update/finish everything and catch up on what I've missed while I've been inactive. DrCeasium (talk) 19:36, May 20, 2014 (UTC)

I'm back!

I have returned out of inactivity! Also, I've made some new bounds on the Xi function, which may or may not actually work, and can be found here. There is a small possibility that the EFAN page may be completed and actually released at some point in the relatively near future. I can't really make any activity promises, but I'll try. DrCeasium (talk) 17:22, August 19, 2014 (UTC)

Cool, can't wait for more of FAN. It seems A WHOLE LOT more thought out than HAN, especially with the naming system. WikiRigbyDude (talk) 18:51, August 19, 2014 (UTC)
wb you'! 19:59, August 19, 2014 (UTC)
Hi Dr. Ceasium, I've found a couple of errors on your page about the Xi function bounds. Fortunately, they actually make the final combinator smaller, so that Xi(41) > G. You can see some combinators I have designed on the Xi function talk page. 05:30, September 8, 2015 (UTC)


dude you should get on the irc channel some time. it's good. -- vel! 21:48, January 23, 2015 (UTC)

Hi Lawrence.

My name is Natan and I read your paper on hyperfacorial array notation and I think it's great work!

In this page( User blog:Natan Consigli/Definition of k-torials - Googology Wiki ) I defined k-torials. It is surly nothing innovative and just a very simple generalization of some sequences.

Do you think it's a good idea if we merge some of my writing with your discovery? Ex. Would you consider changing the rank of the hyper-operators ( ... , [-1] succesor, [0] successor, [1] addition, [2] multiplication, [3] exponentiation, ... so that, for instance, n!1 or n[1]!= n+(n-1)+... instead of n^(n-1)^... etc.). Since n¡=n[n]!= n!n = n![1] would you rather consider it as an extension of the "operatorial" (or whatever would be better calling it) writing n!n = n¡[1] (or something similar) ? The n!m could generally be a bit confusing, changing it to n[m]! could be helpful.

Some of the above changes could result in changing a ton of you work so whatever your final decision is I'll understand.

Best reguards

«Natan Consigli (talk) 22:56, September 2, 2015 (UTC)

Comparing scales

So you've managed to measure your hyperfactorials against Bowers arrays.I'm wondering how your scales stack up against mine,which roll lots of functions into one.(Bowers told me 2 popbled easily beats a gongulus,the popble is not my highest order function).Take a look through the Counting Really,Really,REALLY High web project at if you have time.--L.E./ 08:54, January 8, 2016 (UTC)/

ARE YOU DEAD Billicusp (talk) 20:25, March 2, 2016 (UTC)

EFAN is not so strong

EFAN has limit growth rate \(\psi(\psi_{I(\omega,0)}(0))\). It's not so strong as you think, but still stronger than the n? in HAN.

Your main mistake is that [1(1)[1],[1]] is not \(I\), but \(\Omega_{\psi_I(0)+1}\). Then [1(1)[1(1)1,[1]],[1]] is \(\Omega_{\psi_I(0)2}\) and [1(1)1,[1,2]] is \(\psi_I(1)\). Generally, changing [○(1)〚1◆] into [○(1)〚[1]◆] is changing \(\Omega_\alpha\) into \(\Omega_{\alpha+1}\). To get an \(I\), you need to diagonalize over the second row, and use a [1(1)1(1)[1]]. Then [1(1)[1](1)[1]] is \(\Omega_{I+1}\), [1(1)[1(1)1(1)[1]](1)[1]] is \(\Omega_{I2}\), [1(1)1,[1](1)[1]] is \(\psi_{I_2}(0)\), and [1(1)[1],[1](1)[1]] is \(\Omega_{\psi_{I_2}(0)+1}\).

Another problem is that the limit of \(I(1,0)+1\), \(\Omega_{I(1,0)+1}\), \(\Omega_{\Omega_{I(1,0)+1}}\), etc. is not \(\psi_{I(1,1)}(0)\), but \(\psi_{I_{I(1,0)+1}}(0)\) (using a notation such that \(I(0,\alpha)=I_{1+\alpha}\), \(I(\alpha,\beta)\) is the \(1+\beta\)-th \(\alpha\)-weakly inaccessible, where 0-weakly inaccessible is just weakly inaccessible).

So [1(1)1(1)[1,2]] is \(I_2\), [1(1)1(1)1,[1]] is \(\psi_{I(1,0)}(0)\), [1(1)1(1)[1],[1]] is \(I_{\psi_{I(1,0)}(0)+1}\), [1(1)1(1)1(1)[1]] is \(I(1,0)\), [1(1)[1](1)1(1)[1]] is \(\Omega_{I(1,0)+1}\), [1(1)1(1)[1](1)[1]] is \(I_{I(1,0)+1}\), [1(1)1(1)1,[1](1)[1]] is \(\psi_{I(1,1)}(0)\), [1(1)1(1)1(1)[1,2]] is \(I(1,1)\), [1(1)1(1)1(1)1,[1]] is \(\psi_{I(2,0)}(0)\), [1(1)1(1)1(1)1(1)[1]] is \(I(2,0)\), [1(1)1(1)1(1)1(1)1(1)[1]] is \(I(3,0)\), etc. Thus, the limit of EFAN is \(\psi(\psi_{I(\omega,0)}(0))\). {hyp/^,cos} (talk) 01:04, August 9, 2017 (UTC)

Welcome back. Could you please reply me if you are still familiar with your Extended Factorial Array Notation? {hyp/^,cos} (talk) 13:06, September 2, 2017 (UTC)

We know C(a)esium consists of 1 stable isotope, that is C(a)esium-133.

Are you that one, or are you C(a)esium-137 (No plutonium(III) nitride intended, except this) (Note: C(a)esium is that some write it as Caesium, some as Cesium. How do you write it?)? 10:31, January 12, 2018 (UTC)

my user page

look at it. I love all of these HAN numbers. HaHAHAHAA as guessed your numebrs look nice. might as well use 1,000 in my googolisms that look like yours ;)

—Preceding unsigned comment added by Stevenalexwcr1 (talkcontribs)