10,974 Pages

Hexirp 12 hours ago
2

## (2021-08-05) opinions

Gather opinions.

1. p-shin-daisuki-bot should be blocked for a year. -- C7X, C7X
1. Why? -- People
1. p-shin-daisuki-bot's behavior is WP:SANCTIONGAME. -- C7X, C7X
1. Why? -- People
1. p-shin-daisuki-bot's comments were clearly offensive to Plain'N'Simple. -- C7X, C7X
2. p-shin-daisuki-bot gave Plain'N'Simple eight warnings. -- C7X, C7X
1. If C7X thinks those warnings are invalid, C7X should have voided the warnings and then warned p-shin-daisuki-bot. However, C7X blocked p-shin-daisuki-bot without removing the warnings. -- Kyodaisuu
3. Through private contact, Plain'N'Simple said that Plain'N'Simple was afraid of using this wiki due to recent events. -- C7X, C7X
2. Surely eight warnings at once might be an unusual behavior. However, blocking p-shin-daisuki-bot from posting for …
Literally Legendary 17 hours ago
1

## Number related to Berry's Paradox

Berry's Paradox goes something like this:

The smallest positive integer that can't be described in fewer than fifteen English words.

That got me thinking about ways to define large numbers in fewer than fifteen English words. I wanted to follow these rules:

• Well defined, no paradoxes ("Ten times ten" is allowed but "The smallest positive integer that can't be described in fewer than fifteen English words" or "Zero divided by zero" is not)
• Must be fewer than fifteen English words
• Any words used in your phrase without being defined elsewhere in your phrase must be officially defined (Google Dictionary) so if you wrote "Rayo's function of one million" you would need to use the remaining words to define Rayo's function.
• Use as many punctuation marks…
Literally Legendary 1 day ago
1

## Ideas for symbols to make set theory stronger

These are some ideas for symbols to make a higher order theory which is better at defining larger finite numbers in fewer symbols.

The system of α-order set theories for each ordinal α is defined by LittlePeng9 in this blog post.

We could add a unary function symbol A(x) which denotes the function αostLimit(x) defined by me here that I created which returns αostLimit(x) if x is an ordinal or zero if x is not an ordinal.

We could also add a statement D(x,y,z) which states that x is definable in y-th order set theory in z symbols for an ordinal z≤ω. The truth value of D(x,y,z) is false if y is not an ordinal or if z is not an ordinal which is less than or equal to ω.

We could also add a system which lets you input the formula defining an ordinal x and output …

Mumuji 2 days ago
0

## Penguin Sequence

Let a[n] denote n copies of a joined together as a number (copy notation), so 3[3] = 333, 3[4] = 3333, 4[3] = 444, and 4[4] = 4444. In case of zero, n[0] = n[1]

Define the p(n) as follows:

Apply the steps in order, when a step is executed, jump back and repeat the steps.

p(n+1) = n if n = 0

p(n+1) = n[p(n) -1] * n[p(n)]

p(2) = 2[p(1)-1] *2[p(1)] = 2[1-1] * 2[1] = 2 *2 = 4

p(3) = 3 * 3[p(2)-1] *3[p(2)] = 3 * 3[3] * 3[4] = 3 * 333 * 3333 = 3329667

this is only p sequence.

pe(n+1) = p(n) if n = 0

pe(n+1) = pe(n)[pe(n) - 1] ^ pe(n)[pe(n)]

pen(n+1) = pe(n) if n = 0

pen(n+1) = pen(n)[pen(n) - 1] $$\uparrow\uparrow$$ pen(n)[pen(n)]

peng(n+1) = pen(n) if n = 0

peng(n+1) = peng(n)[peng(n) - 1] $$\uparrow^3$$ peng(n)[peng(n)]

Do you see the sequence?

It is simi…

Msiajoe74 2 days ago
1

## Extended Veblen Function

Veblen function is fascinating, it creates ordinal up to LVO. But could it go farther than that? I think so; let me explain.

1. We use @ to indicate the number of 0's in SVO
1. = 𝛗(1@ω)
2. =｛𝛗(1,0), 𝛗(1,0,0). 𝛗(1,0,0,0), ...｝
2. We then use @@ to indicate the ω-th term in LVO sequence
1. = 𝛗(1@@ω)
2. =｛ω, 𝛗(1@ω), 𝛗(1@𝛗(1@ω)), ...｝
3. =｛ω, SVO, 𝛗(1@SVO), ...｝
3. From there we can define SEVO
1. = 𝛗(1@@@ω)
2. =｛ω, 𝛗(1@@ω), 𝛗(1@@𝛗(1@@ω)), ...｝
3. =｛ω, LVO, 𝛗(1@@LVO), ...｝
4. For non-negative integer a: 𝛗(1@@O+a+1) = ...𝛗(𝛗(𝛗(1@@O+a)@@O+a)@@O+a)... , where O denotes any ordinal.

1. Define @ =/1\, @@ =/2\, @@@ =/3\ and so on.
2. Then SVO = 𝛗(1/1\ω), LVO = 𝛗(1/2\ω), SEVO = 𝛗(1/3\ω) and so on.
3. LEVO
1. = ...𝛗(1/ω\𝛗(1/ω\𝛗(1/ω\ω)))...
2. =｛ω, 𝛗(1/ω\ω), 𝛗(1/ω\𝛗(1/ω\ω)), ...｝

My guess is, LEVO could at least reach B…

DAno80 4 days ago
3

## A Function on the 3x+1 problem

I am one who worked on this, and i decided to make a Function on it, so the 3x+1 problem is:

Pick a Number, i choose 7, we are going to apply these 2 rules:

-If the Number is odd, multiply it by 3 and add 1 to the result.

-If the Number is even, divide it by 2.

So 7 would be:

7->22->11->34->17->52->26->13->40->20->10->5->16->8->4->2->1.

Now, this Function, which i will call T(n), represents the Number of steps it takes for n to reach 1 with these rules, since it hasn't been proven that it ends in a 1 for all Numbers, it might reach Infinity, but these are some values:

T(1) = 1

T(2) = 2

T(3) = 8

T(4) = 3

T(5) = 6

T(6) = 9

T(7) = 17

T(8) = 4

T(9) = 20

T(10) = 7

Now, here we consider even the First Number as a step, i created this because for even small outpu…

Literally Legendary 6 days ago
1

## Computable numbers vs uncomputable numbers

Technically every number is computable, as a computer program can take the number before it and add 1. However, usually when people talk about computable numbers, they mean numbers defined in terms of a computable function. Today I would like to define what it means for a number to be computable (kind of).

A number is computable if Rayo-naming it in the least amount of symbols uses a string of symbols which can be broken down into strings A, B, and C where B is a string which defines another computable number and the other strings A and C together make a computable function.

Kanrokoti 6 days ago
1

## 2-shifted Subspecies Primitive psi Function

• 1 Overview
• 2 2-shifted Subspecies Primitive psi Function
• 2.1 Notation
• 2.2 Abbreviation
• 2.3 Ordering
• 2.4 Code function
• 2.5 Ascension function
• 2.6 Cofinality
• 2.7 Fundamental Sequence
• 2.8 FGH
• 2.9 Limit of the notation
• 2.10 Standard Form
• 2.11 Naming

We define 2-shifted Subspecies Primitive psi Function. This notation is based on Ordinal Notation Associated to Extended Buchholz's OCF defined by p進大好きbot, and extend it by uniting Subspecies Primitive psi Function and 2-shifted psi Function. In order to avoid an infinite loop, I omitted the condition $$a = c$$ in the C…

Mumuji 6 days ago
3

## 200!

(Well technically 215 due to errors with the blog count, but whatever!)

I came up with a short program to compute the FGH in python! (Without ordinals of course!)So, a challenge of sorts:

Make a python program with the following rules:

Rules:

• Terminates
• Finte output
• Uses no more than 512 characters (Basically all characters on a keyboard excluding whitespace)
• No abusing whitespace (If you do something like coutn the whitespace)
• No value can be greater than 10
• Output MUST be printed (print also counts to the character count)
• Use python (not python3)
• That's it

Special thing:

a part of a secret:

"My"

Part 2 at 400, 3 at 600, etc.

Thefamousarthur 6 days ago
0

## My extension of UNOCF

c(1) = H c(2) = J c(3) = L We can have things like c(9) = O. Then comes O{2}, O[2], and each time there was something new. So there will be one here too. Then there's c(10), called P, adding another thing again. Then c(11) = V, then c(12), c(13), and we can just keep going with c(n). Then there's c(ω), c(c(1)). Then there's c() a thing called ∞_0, 1, keep nesting. We now introduce c_2, then c_3, and an infinite nesting of c's is not the end, though.

This is where we make an H function to denote the symbols in the subscript of c. Then after H(H(H(H(...)))), there's H_2, then H_3, H_H, infinite nesting. This comes L^3, then L^4, L^ω, L^L, and so on.

Msiajoe74 6 days ago
1

## Veblen Function primed

In googology, Veblen function is one of the most popular that defines ordinal fundamental sequence. Here I want to redefine it into something more powerful. 1- Ordinal Arithmetic using Hyper Operators

1. For positive integer a and Ordinal O:
1. O《1》a = O+a
2. O《2》a = O*a
3. O《3》a = O↑a
4. O《4》a = O↑↑a
5. O《5》a = O↑↑↑a
6. And so on.
2. For positive integer b and ordinal P:
1. O《b+1》c+1 = (O《b+1》c)《b》O
2. O《b+1》P+c+1 = (O《b+1》P+c)《b》O
3. Other rules shall follow standard ordinal arithmetic and up arrow's rules.

2- One-variable

3- Two-variable Veblen Function primed

1. The function is right associative.
2. φ'(0,c+1)
1. = φ'(0,c)《ω》ω
2. =｛φ'(0,c)《1》1, φ'(0,c)《2》2, φ'(0,c)《3》3, ...｝
3. =｛φ'(0,c)+1, φ'(0,c)*2, φ'(0,c)↑3, ...｝
3. φ'(1,0) = ... φ'(0,φ'(0,φ'(0,0))) ...
4. φ'(1,c+1) = φ'(1,c)《ω》ω.
5. φ'(1,O+c+1) = φ'(1,O+c)《ω…
Literally Legendary 6 days ago
0

## New function?

Warning: Ill defined and/or naïve extension

Elevator(n) = RayoFLTO(n) with this system for Rayo functions for each ordinal and FLTO is First Large Theory Ordinal based off of this system of set theories for each ordinal. I think I might have come up with something similar to User blog:LittlePeng9/Higher order set theory if I knew more about universes of sets and stronger universes of sets which range over subcollections of the previous universes of sets.

Googolevator = Elevator(10^100)

Googolevatorplex = Elevator(10^10^100)

High Elevation = Elevator(Pacific((4^^4)^4^^4(4^^4))) where Pacific(n) is defined here and a^bc indicates arrow notation.

And yeah the axioms are ZFC

Literally Legendary 7 days ago
1

## Pillar Function

Recursive Array Function Language has these symbols:

S 0 1 2 3 4 5 6 7 8 9 ( ) , = > < : ; and countably many variable and function symbols.

The , is to separate inputs of a function, the : is for conditions after statements, and the ; is to separate statements.

S is Successor function by default.

Pillar(n) is the smallest natural number greater than all numbers that can be obtained by inputting 10^n in any terminating function defined with n symbols or less in Recursive Array Function Language.

Pillar(f(x),n) is the smallest natural number greater than all numbers that can be obtained by inputting 10^n in any terminating function defined with n symbols or less in Recursive Array Function Language with S being f(x) instead of Successor function…

GamesFan2000 7 days ago
2

## Issues concerning the deletion of the page for the Discord server

https://googology.wikia.org/wiki/User_blog:GamesFan2000/This_community_has_gone_to_hell...?commentId=4400000000000037568

Ubersketch commented in my most recent post stating that they thought that Kyodaisuu's deletion of the page regarding the Discord server was unjust. The worrying part about this was that Kyodaisuu only consulted with four other community members before going through with this. Uber tried to revert the page and open dialogue with Kyodaisuu, but to no avail. I'm requesting a larger dialogue for this situation so we can get a more general opinion. I would've posted this on Kyodaisuu's talk page or my own talk page, but I don't know how to use this version of the source editor.

P進大好きbot 8 days ago
2

## Analysis on 四関数

This is an English translation of my Japanese blog post on analysis of 四関数 submitted to a Japanese googology event.

In order to simplify convention in analysis table, I introduce abbreviation for $$T$$ and $$DT$$.

before
after

Although there is no clue of a proof, I am expecting that $$(OT, MultiSoul 8 days ago 0 ## My Custom Googol Base Multipliers!!! 1. Googolkeed - 10^2,400,000 2. Googolceed - 10^4,800,000 3. Googolpaur - 10^9,999,999 4. Googolboop - 10^11,222,333 5. Googoljemn - 10^2,000,000,002 6. Googolsowm - 10^3,111,111,111 7. Googolwhat - 10^ C7X 8 days ago 4 ## Recent events 2 Here's an incomplete, sourced list of some points on the PBot/Psi situation, leaving out those from the Cloudy situation last month. 1. Since Psi was already getting frustrated in the comments, PBot's remarks , search "Why don't you apologise for the other issues?" 2. link, search "please judge him" 3. link, search "it is inappropriate for you to label that the OP cannot do it" 4. link 5. link 6. link 7. link 8. link Since you will most likely read this, please reflect on what you've done. It's not sufficient to brush this section off using others' behavior either. This is serious business, and taking people's words out of context does nothing to alleviate this drama, but instead makes it worse and adds more tension. Veteran users such as Username and Psi have already quit… Hexirp 8 days ago 1 ## (2021-07-28) Let's not provoke them The person you were discussing it with may have a terrible outburst against you. You may use sarcasm, provocation, etc. to fight back. However, this will give the other person a chance to criticize you. For p-shin-daisuki-bot, Yukito, and others. GamesFan2000 8 days ago 3 ## This community has gone to hell... I wanted to come back to this community for a moment, and that was the exact moment it went to hell. There's an extreme disconnect between what goes on here and what goes on with the Discord server. It resulted in some less than friendly exchanges between myself and C7X when I checked the wiki-talk channel of the Discord a few days ago. I feel like a pawn in a much larger conflict which I don't understand. Username5243 has made a blog post stating that they believe that P-bot has made himself a dictator who can't be criticized without risking a warning or blocking, announcing their departure from the Wiki. P-bot has somehow managed to turn a significantly powerful section of the western community against him, fracturing the two main platfo… Username5243 8 days ago 4 ## Pbot, this is ENOUGH! I'm leaving! Issues on the wiki have gotten out of control ately, quite frankly. Recently, P-bot has seized de-facto, if not de-jure, absolute power on the wiki through gaming the attempted new policy, and issuing "harassment" warnings to anyone who even mildly criticizes him, and once you start arguing with him he's all too likely to claim harassment rather than try to genuinely argue with him. He's also criticized the Discord, which while not exactly in good shape these days, I'd hardly argue is the den of intolerance and even racism certain people on here seem to have been prompted to believe it is. Sure, it doesn't take itself quite as seriously as this wiki, and most users there do this stuff (gasp!) for FUN, not in an attempt to get themselves take… MultiSoul 9 days ago 3 ## My Custom Numbers! Twelvetyplex, 10120 (twelvety + -plex) Ungoogolillion, ARsygo 9 days ago 5 ## About FandomDesktop thingy Well, is it me, or the Wiki reverted from FandomDesktop to the Oasis skin, for no reason? Note: I'll post a screenshot for the proof. Tetramur 10 days ago 5 ## Big functions Can someone tell me about fast-growing computable functions not based on exponent or factorial? MultiSoul 10 days ago 1 ## My List Of Illion Numbers!!! • 1 Dictionary -illions • 2 Other -illions • 3 Bower's Extended -illions • 4 My extended illions (inspired by Nivarna Supermind) • 5 My Extended illions (P2) • 6 Objects with -illion • 7 Arabic Alphabet with -illion • 8 Greek Alphabet with -illion (with a bit of more arabian alphabet stuff) • 9 Planets with -illion • 10 Some more -illions (with some Undertale characters) • 11 Morgan Burke & Miscellanious Jargon Prefixes with -illion • 12 Cookis Fonster Prefixes with -illion • 13 SEPS with -illion • 14 Tier Jumpers • 15 Greek Quantitative Prefixes with -illion • 16 Roots with -kisillion • 17 EMPS (with -kis) with -illion • 18 Spanish Numbers with -kisillion • 19 Renamed Tier 4 illion roots with -illion (with BAT4432's extended illions) • 20 More Of BAT4432's extended illions • 21 Latin/English Numbers with -illion • 22 Mega T… Literally Legendary 10 days ago 0 ## Computable number for once m^1n = m^n; m^n1 = m; m^n+1p+1 = m^n(m^n+1p); g(0,n,p) = p; g(m+1,n,p) = n^g(m,n,p)n; g1(n) = g(n,n,n) Glacier = g1(65536) Kind of like Graham's number I guess because Graham's number can be expressed by g(65,3,4) BiGlacier = g1(2^32) TriGlacier = g1(2^64) QuadriGlacier = g1(2^128) QuintiGlacier = g1(2^256) HexaGlacier = g1(2^512) HeptaGlacier = g1(2^1024) OctoGlacier = g1(2^2048) NonaGlacier = g1(2^4096) DecaGlacier = g1(2^8192) Globalwarmingnumber = 0 - g1(65536) Glacier Prime = ⌊A^(g(⌊A^(⌊A^65536⌋)⌋,⌊A^65536⌋,65536))⌋ where A = Mills' Constant Literally Legendary 10 days ago 2 ## What is the fastest growing function that grows slower than Rayo(n) that has been defined so far? Of all the functions on the wiki it appears to be the Infinite Time Busy Beaver function but has anyone defined a more powerful function in a blog post? Ynought 10 days ago 0 ## Various types of fast growing functions • 1 Introduction to types of fast growing functions • 1.1 Recursion • 1.2 Games • 1.3 Formal languages • 1.4 Turing Machines • 1.5 Graphs • 1.6 Others This post is mainly for newer people. It will not introduce any new ideas and will mainly show some of the ones that are already well established to create fast growing functions. The idea behind this category is to repeat an operation, say \(n+1$$, really often. Some of the most notable functions and notations in this category are SAN or the fgh. There are many sub-categories like Difference sequence systems and array notations among other things. A lot of functions defined by users in this wiki can be found in this category.

This is relatively self explanatory, but this category includes games that can last for many ro…

Kyodaisuu 11 days ago
0

## List and program of -illion numbers

I made a page of -illion numbers. It has a complete list of Conway-Wechsler system and modified system up to milliducentillion (1200-illion) and can be used as a perfect source for these numbers. For example, it is used as a source at Septuagintacentillion.

Fish. Conway's zillion numbers July 25, 2021

I also published a software in the same page to obtain a name of arbitrary N-illion number, which was used to produce the table in the page.

RudyStaysForever 11 days ago
0

## Binary Table

Literally Legendary 11 days ago
1

## Q

I define Q-BB as the least value of the Busy Beaver function which cannot be proved under ZFC.

I define Q-FF as the least value of the Maximum Shifts function which cannot be proved under ZFC.

I define Q-XI as the least value of the Xi function which cannot be proved under ZFC.

I define Q-ITBB as the least value of the Infinite Time Busy Beaver Function which cannot be proved under ZFC.

DAno80 11 days ago
2

## An Array Notation i cannot give the name

[a] = a

[a,b] = a->b

[a,b,c] = a->a->a->a->.....->b->b->b->b (with c Chained Arrows and with half a's half b's, if the number of a's and b's is odd, then n+1 a's).

[a,b,c,d] = a->a->a->a->...->b->b->b->b

_______________________ : : with d levels = n(d) (n's Function). : __________________ a->a->..->b->b _____________ a->.....->b _________ c

[a,b,c,d,e] = n(n(n(......(n(n(d))...)) (with e n's). [a,b,c,d,e,f] = n^n^n^n^......^n^e(d) (with f n's and "^" is the Iteration of n(x)).

We can now define this:

a(b) = [a,a,a,a,a,......,a,a,a] (with b a's).

Now i introduce Firs…

Mumuji 12 days ago
0

## E system

199. Special thing at 200.

To lighten the mood, here is a bad e system i made.

This started as me listing out numbers: 1,2,3,4,5,6,7,8,9,10.

Then, 100, 1000, 10000, and so on until I got tired.

I use the E notation ($$Ex = 10^x$$): E20, E30, E50, E100, E1000, and so on.

Then, EE10, EE20, EE30, EE50, EE100, EE1000 and so on.

I went on : EEE10, EEEE10, EEEEE10, EEEEEE10.

But this was boring.

So i invented the operators.

E^x = $$\underbrace{EE\cdots EE}_{x}x$$.

E^10,E^20, E^30, E^40…. E^E10, E^E^10, …

But this would do me no good.

So, came the ^ operators.

^######…### = ####^#

like this.

So I went on.

$$E\underbrace{\#\cdots \#}_{n+1}\hat{ }\#x = E\underbrace{\#\cdots \#}_{n}\hat{ }\#\underbrace{\#\cdots \#}_{x}x$$

E##^#10, E###^#10, E####^10….

Literally Legendary 13 days ago
0

## New ordinal function idea

In http://www.polytope.net/hedrondude/oblivion.htm Jonathan Bowers mentions this idea "heck what about LVO-order set theory (assuming this is definable.)"

If someone makes a system of set theories with each one assigned an ordinal less than the ordinal of any stronger set theory and greater than the ordinal of any weaker set theory, with each countable ordinal having a set theory, where 0-order set theory is first order set theory, that would be needed for my idea to work.

If there are countably many set theory formulas in any order set theory, then there are also countably many ordinals which can be defined in that theory.

αostLimit(α) is the least countable ordinal greater than all countable ordinals definable in α-order set theory.

First La…

LightLightsLarLabLiblas 13 days ago
1

## The aftermath

This is the last blog post I'll be posting.

It seems that the situation has finally calmed itself down, but this does not mean I'm willing to return. I said I will not contribute, and I will stick by that ruling. I have other things I should be working on anyways, so there isn't much motive for me to return.

Plain'N'Simple has been blocked for 3 months.

C7X is disabling their account(?)

Hexirp was given administrator rights by ARsygo.

P進大好きbot was unblocked by Hexirp.

I do not intend for harassment towards any of the users above.

Also, please don't message me on my talk page(s).

GamesFan2000 13 days ago
3

## Final thoughts

With Hexirp blocking Plain'N'Simple, the situation seems to have finally resolved itself. Unfortunately, the events that transpired have left a bad taste in all of our mouths. I'd like to leave some final thoughts for the users who were involved in the events in one way or another:

P-bot - I sincerely believe that you have done nothing wrong. Most of us greatly appreciate your insight and advice. I have always admired your work, and I have a lot of respect for you, especially after our conversations on the LNGN. I hope that nothing like this ever happens again, because you not being here could spell disaster for the community at large.

Plain'N'Simple - Just to be clear, I don't wish for any harassment to come your way. Your transgressions do…

Mumuji 14 days ago
0

## In light of recent events

Blog post 198.

I am not going to comment on most recent events due to not because I don't care, but rather I do not want to cause more arguemets with opinions. I will not attempt to engage in such conversations, as a new debate will be equivalent to putting salt on a wound. As of this, I will not be stating my opinions, due to any possible harm. However, I will post my current opinions in this blog post, and if you do not like them, please do not actively attempt to argue.

Opinion 1

The reason that this arose is because most people do not like accepting their fault. It's human nature.

Opinion 2

pbot is right. Plain and simple should be blocked.

Hexirp 14 days ago
1

## (2021-07-22) p進大好きbot and Plain'N'Simple

1. I warn P for removing the warning.
2. I determine if the warnings are valid. If more than three warnings are valid, I block Plain'N'Simple.
3. I remove harassments that have been the subject of valid warnings.

I did the following.

1. I warned Plain'N'Simple.
2. I have scrutinized the warning. Five of the nine warnings were valid, so I blocked Plain'N'Simple.
3. I have removed the sentences pointed out by the five warnings that I have determined to be valid.
GamesFan2000 14 days ago
1

## My opinion on Plain and C7X

DISCLAIMER: The opinions disclosed in this blog post are constructed based on what I've heard from all parties involved in the events that unfolded recently and my understanding of what happened. These are my opinions, and they don't reflect the opinions of anyone else. If you do not agree with something that is said in this post, please discuss your thoughts in the comments. I do not condone harassment of any kind, and I do not wish for any transgressions to be taken against Plain'N'Simple and C7X beyond any actions taken by the administrators in accordance with FANDOM's guidelines. As far as I'm aware, both of the users in question have left the community, so it might not be necessary for the administration to take action against them. T…

Mumuji 14 days ago
0

## pinguin moment

This is my 197th blog post. Let all terms below belong into set $$C$$ unless specified. We create set C using set builder notation. $$C = \{x|0 0 \(C(a,b+1,c) = C(f(a),b,f(c)),\; f(n) = n\uparrow^nn$$

for b = 0

$$C(a,b+1,c) = a^c$$

$$a\{b\}c = C(a,b,c,b) = a\{b\}^1c$$
if b > 0 and d > 0

if b = 0
$$a\{b+1\}^{d+1}c = \left. \begin{matrix} &&\underbrace{a\{a\{\cdots \{a\}^d\}^d\cdots\}^d}\\ & &\underbrace{a\{a\{\cdots \{a\}^d\}^d\cdots\}^d} \\ & & \;\;\underbrace{\quad\quad\;\; \vdots \quad \quad \;\;}\\ & & \underbrace{a\{a\{\cdots \{a\}^d\}^d\cdots\}^d} \\ & & b\quad a's \end{matrix} \right \} \underbrace{a\{a\{\cdots \{a\}^d\}^d\cdots\}^d}_{\text{b copies of a}}$$
The underbraces above denote the amount of a's.

$$\{\} = 1$$
$$\{a\} = a$$
$$\{a,b\} … P進大好きbot 14 days ago 0 ## On the Recent Incident in Googology Wiki Hello. I wrote a Japanese blog post explaining the recent incident in Googology Wiki, because I was unable to explain to you what actually happened due to the blocking. Roughly speaking, I was suffered from excessive harassments from Plain'N'Simple, and our admin ARsygo kindly asked Plain'N'Simple to stop the harassments. Although Plain'N'Simple admitted the fact about what Plain'N'Simple did, Plain'N'Simple refused to apologise for the harassments. Therefore ARsygo proposed me to put the warning templates to Plain'N'Simple, and I followed the suggestion. After that, Plain'N'Simple seems to have asked C7X to block me by privately insisting something like that the report of harassments made him unpleasant, and C7X obeyed the request. I note … Hexirp 15 days ago 1 ## (2021-07-22) Logo This is a modification of User_blog:Mumuji/test. Mumuji 15 days ago 2 ## test $\text{Googology}\uparrow\uparrow\omega \text{iki}\\ \{\text{The,large,number,encyclopedia}\}$ ARsygo 15 days ago 3 ## Updates on this wiki Hello there, once again, I'll deliver an update for this wiki. Is there anyone not yet migrated to the new FandomDesktop? I actually changed the colour of the Wiki, to the original, in the theme designer (only admins allowed to edit), by importing the previous themes into the desktop. Anyway, some of the unsourced and/or unlicensed contents have been deleted, via the recent changes page. Update: the cleanup is currently in progress. Literally Legendary 15 days ago 1 ## What is the system of fundamental sequences for Takeuti-Feferman-Buchholz ordinal? I want to use it in one of my functions. Hexirp 16 days ago 0 ## (2021-07-20) p進大好きbot and Plain'N'Simple I will explain the conflict between p進大好きbot (pしんだいすきbot, p-shin-daisuki-bot, p-shi-n-da-i-su-ki-bot, "the bot beloved by p-adic numbers") and Plain'N'Simple (also PsiCubed2). p-shin-daisuki-bot is giving the explanation in Japanese. However, there is no explanation in English. So I will give an inadequate explanation. • 1 from mathematical arguments to emotional bickering • 1.1 timeline • 2 requesting • 2.1 timeline • 3 summon • 3.1 timeline • 4 cleaning • 4.1 timeline Plain'N'Simple was studying Rayo's number. p-shin-daisuki-bot said it contains errors. There was a long discussion about this. p-shin-daisuki-bot said that Plain'N'Simple was making a lot of mistakes, and no amount of explanation would improve things. p-shin-daisuki-bot told Plain'N'Simple to read a basic te… Bogush4 16 days ago 0 ## Chain Notation The thing is, I wanted to make a updated version of the 1D Line notation, so I did. 1. (A,B)=A*B 2. (A,B,C)=A^(C)B 3. (A,B,0)=(A,B)=A*B 4. (A,B,C,D,...,X,Y,Z)=(A,B,C,...,X,Y,(A,B,C,...,X,(... ...,X,Y)))... ...) With Z chains 5. (A,B,C,D,...,X,Y,1)=(A,B,C,D,...,X,Y) 6. (1,B,C,D,...,X,Y,Z)=1 • Googol=10^100=(10,100,1) • Googolplex=10^10^100=(10,(10,100,1),1) • Gopgol=10^^100=(10,100,2) • Gopgolhex=F^^FF=16^^256=(16,256,2) • Gopgolhexlex=F^^F^^FF=16^^16^^256=(16,(16,256,2),2) • Floplol=(10,100,3) • Bongol=(10,100,5) • Dekic=(10,10,10) • Gongol=(10,100,10) • Bellgol=(10,100,100) • Towergol=(10,100,1000) • Churchgol=(10,100,10^6) • Goodugol=(10,100,(10,100,1)) • Gootrigol=(10,100,(10,(10,100,1),1)) • Matha=(10,10,10,10) • G(64)=(3,3,4 • Ex-Matha=(10,10,10,100) • Duex-Matha=(10,10,10,1000) • Triex-Matha=(10,10,10,10000) • Dec-e… Mumuji 17 days ago 0 ## Things to do to farm edits (That are useful) All you need is time. Go to any of Sbiis's cascading/hyper/extended cascading/whatever e number's catagory, randomly click on a link, if it has a approximation, pick again, than when you find a page without an approximation, find the reignment it is in, (by searching the name, it should appear in the results), add the approximation (If it is below \(\varepsilon_0$$, add a omega to make it become hardy.

Mumuji 17 days ago
0

## Yoy

Current most active users- top 3: User:C7X User:ARsygo me

Hexirp 17 days ago
4

I will do the following in one days. Please let me know what everyone on this wiki thinks.

1. Revert Special:Diff/329789.
1. Reason: People want to know what p-shin-daisuki-bot actually did.
2. Reason: I would like to verify that p-shin-daisuki-bot's warning is valid.
3. Reason: This edit was not authorized by any administrator.
1. Supplement: The policy stipulates that removal of warnings requires administrator permission.
2. Unblock p-shin-daisuki-bot.
1. Reason: In User_blog:Hexirp/(2021-07-17)_Blocking, there were no opponents.

I did it.

1. Special:Diff/330423
2. log

Thank you all for taking the time to comment. Hexirp (talk) 11:45, 20 July 2021 (UTC)

This request has been closed. If you have an opinion, I encourage you to use the talk page.

Hexirp (talk) 09:02, 22 July 2021…

Literally Legendary 17 days ago
1

## 1st order set theory & 2nd order set theory: What is the difference?

I also want to know the difference between 2n-order set theory and 3rd order set theory, etc.

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