recursal/Fanatic-Fandom huggingface dataset:
PIL+

PIL+ is a number that uses the thought level system to surpass even Weak Omnicollapse in its magnitude. Everything here is collapsed to level 2.

## Systems

A system is defined as any combinations of properties on any thought level that has the ability to create abstract concepts of size (AKA numbers). For example, TEA is a system, humans are a system (because we make hypergoogology), omnipotent gods that exist on authorlock would be a system... and so on.

## Definition

PIL+ is the limit of every system on every level, PIL+ cannot be described on any thought level as it surpasses the concept of thought levels altogether, collapsed to level 2. We can think of it like the limit of the limit of thought levels, it comes after a never ending sequence of "limit of level 0, limit of level 1...... limit of level w, limit of level w+1..... limit of level PIL.... limit of level PIL+.........." (this means it is past its own thought level), then this is collapsed back through every level back to level 2 just so that it can actually exist as a concept.
Outerconst

Outerconst is a constant with some properties outside of the normal instance of mathematics, some not, therefore allowing it to be comparable to regular numbers while also completely breaking how infinites work. The instance Outerconst is contained within is "B-Mathematics", while the traditional instance is "A-Mathematics".

## Notations

For reference, the following notations will be used:

B

x

=

{\displaystyle B\_{x} =}

 X from A-Mathematics translated to B-Mathematics

## Definition

Outerconst is defined as

B
0

{\displaystyle B\_0}

, or the B-mathematical counterpart of 0. The axioms of B-mathematics are:

* For a predicate with arbitrary amount of arguments

P

{\displaystyle P}

,

P
(
a
,
b
,
c
,
.
.
.
)

{\displaystyle P(a,b,c,...)}

 being true implies that

P
(

B

a

,

B

b

,

B

c

,
.
.
.
)

{\displaystyle P(B\_{a},B\_{b},B\_{c},...)}

 is also true.
* For any A-mathematical

x

{\displaystyle x}

,

B
x

{\displaystyle B\_x}

 is always B-mathematical and **not** A-mathematical.
* For any A-mathematical

x

{\displaystyle x}

 and B-mathematical

y

{\displaystyle y}

,

y
>
x

{\displaystyle y > x}

.
* The domain of

B
x

{\displaystyle B\_x}

 is all of A-mathematics, and the range is all of B-mathematics.
* If

x

{\displaystyle x}

 is not larger than any B-mathematical number and isn't B-mathematical, than

x

{\displaystyle x}

 is A-mathematical.

## Expansions

Outerconst's definition can be easily be extended to allow for bigger numbers, such as:

* A-Mathematics and B-Mathematics can be generalized into an infinite chain of mathematics.
* For weaker extensions, Outerconst can be just added or incremented etc. like a normal number

## Symbolism

Outerconst's glyph resembles a triangle, the typical symbol for a hierarchy, being crossed out with a line. This denotes the removal of hierarchial bounds, which Outerconst does something similar to (but redefining instead of deleting).
Dedication (ණ)

Dedication is a number by Icosalord attempting to be within Class 5.

## Definition

Dedication is beyond any thing with any property, for all definitions of this sentence. It doesn't matter if the property is false or inapplicable for the thing, Dedication is beyond that thing. As Dedication has the property of existing, Dedication is also larger than itself.

(updated to be way larger)
Zeroids

Zeroids are numbers that are defined as signless. Zeroids are greater than all negative numbers, but less than all positive numbers. Some zeroids are bigger than 0, whereas some are smaller than 0.

## Underscore Notation

This is currently considered the "best" theory for a way of creating zeroids. This stems from a theoretical number \_ such that \_\*0 = \_ & \_ is not equal to zero. To extend that, we can then apply the same process on more numbers \_n\*\_n-1 = \_n, \_n is not equal to \_n-1. We can assert that these exist via TEA.

## Examples

* \_ (definition in previous section)
* \* (a state in combinatorial game theory)
Anadromic Limit

Anadromic Limit is a number created by Goodels and TheGoogologist. It combines the concept of 'hypersystems' from Conceptual Breaking Point and the concept of 'hyperuncomputability'.

## Hyper-Recursion

Hyper-Recursion is where you take a concept of a certain grouping of concepts, and extend the idea further due to some sort of inaccessibility. Larger systems of Hyper-Recursion can form, where the Hyper-Recursion itself is Recurred with some sort of extension. eg. the concept of hypersystems being extended to where the tiers of the system start at the level inaccessible from any hypersystem.

## Hyper-Recursive Systems

A hyper-recursive system is defined as any grouping of concepts (a system, hypersystem, or other extensions that could be made, eg. the grouping of concepts that cannot be defined by any hypersystem) that could have some sort of hyper-recursion applied to it to go further.

## Definition

Anadromic Limit is described as the number least number such that it could not be described by any concept contained within any Hyper-Recursive System. Note, this would be bigger than simply "The number where no concept from any groupings of concepts could describe its size", as there is a concept of the groupings of concepts, the concept of the grouping of concepts merely existing within the first hypersystem. This definition is written beyond all thought levels but collapsed to level 2.
Interpretable+ (i!)

Interpretable+ (i!) is the final ! number. It is a tier VI number.

## Worldview Concepts

Abstract concepts do not exist within a vacuum. Let's take the abstract concept of 3, this does not truly mean anything until it is interpreted by someone or something (arguably). An abstract concept could be interpreted in many different ways, this does not mean that they are different concepts. The way someone or something thinks and views thigns will change the way a certain concept exists. For example, 3 interpreted by an algorithim simply means the complete abstractification of 3ness itself, but for us humans 3 usually means 3 distinct things (3 apples, 3 numbers, 3 notes ect...). This shows that concepts are not truly objective and have variations depending on the interpreter's worldview. I will call this phenomena *Worldview Concepts*.

## Subjective Definitions

Worldview concepts affect definitions. They can result in a different meaning depending on which interpreter. It is important to note that interpreters are not only people, animals or things, subjects (for example Hypergoogology) are also interpreters in a way, meaning they are also subject to worldview concepts. An example of this is the concept of "the number beyond all others", within Hypergoogology this is a valid definition and somehow still not actually the number beyond all other numbers, but in mainstream mathematics this is meaningless and invalid, this concept itself being put through another layer when interpreted by a conscious being.

## Every Number is Personalised (DO NOT RESEARCH!)

This means that some numbers are bigger than others only depending which interpretation layers they have gone through, within formalised or semiformalised systems there is no further interpretation levels that could alter them, but these systems themselves are interpreters. This shows that definitions can change meaning and size within certain systems, and in completely informal systems they can change depending on the individual subinterpreter.

## inef.[ ]

For a concept C, inef.[C] is the deeper truth that C stands for. Where C might me misinterpreted by interpreters, inef.[C] is the core idea that C represents regardless of any interpretation. It is C taken at the most face value it can be, without subjecting it to any interpretation, and if an interpreter interprets inef.[C] as their interpretation of C then they are not interpreting inef.[C].

## hgi.[]

inef.[For a concept C, hgi.[C] is the Hypergoogological interpretation of C].

## Definition

* inef.[If i! is deemed smaller than some other number by an interpreter, they are not interpreting i!]
* inef.[inef.[i!] = hgi.[i!]]
𐆓₀

𐆓0 is based off The Successor Fixed Point.

## Definition

I will call The Successor Fixed Point (SFP) s0. sn+1 is the next number truly greater than sn that is also a fixed point of the successor function. 𐆓0 is now defined as the first fixed point of the successor function such that it cannot be represented by sn for any n, including 𐆓0 itself.

This idea is continued in 𐆓-MAX.
Outdated HG Archive

**Outdated HG Archive**
NOTICE: We have moved to a new wiki from this one to get a fresh start on concepts and to rewrite the definitions. This means this wiki will not recieve any more updates and is quite outdated. For the new wiki, see here.

## Introduction to Hypergoogology

Hypergoogology is the study of finding the largest possible concepts of abstract sjze often through more philosophical means than mathematical ones. Simply put, massive numbers beyond all comprehension.

Unlike fictional googology, Hypergoogology requires its numbers to have some kind of definition, for the fictional googology wiki, see here.

When creating posts, please don't spam create posts, please make sure your number has a definition and don't make any claims about your number being "the biggest number possible" because we can always surpass any number, that's the point.

For the exact definition of hypergoogology, see here [will be added soon].

Hypergoogology is a type of hyper-ology, to see Serge's paper on general hyperological principles, see here.

Discord: see here

Have fun.

## Info

* List of Hypergoogological Numbers.
* List of Hypergoogological Concepts.
* List of Undefined Numbers,
Numbers Defined in QDAN

quandale dingle's array notation here

## The Rat Segment: {0,1} to {0,0,1}

qwergil : {0,1}

jilgerat: {{0,1},1}

spinning jilgerat: {{jilgerat,1},1}

doubly spinning jilgerat: {{spinning jilgerat,1},1}

n-spinning jilgerat: {{n-1 spinning jilgerat,1},1} where 2-spinning jilgerat is doubly spinning jilgerat

pijifedes: {0,2}

jrewirical constant: {2000,2}

habsasea: {0,3}

hadjiko; {0,4}

jahfifihs: {0,5}

tiriat: {0,{0}}

quiriat: {0,tirrat}

penrait: {0,quiriat}

heraiat: {0, penrait}

serpiat: {0, heraiat}

ocratiat: {0, serpiat}

neoniat: {0, ocratiat}

dercaiat: {0, neoniat}

n-iat: {0, (n-1)-iat} where tiriat is 3-iat

the biggerst rat: {0,0,1}
Simplification Fallacy

Simplification Fallacy is a common misunderstanding of Hypergoogology. It is where someone generalises the current trend of Hypergoogology and assumes that the way things develop now will be the way things develop in the future. It is also where someone assumes that the current biggest/best thing will be the biggest/best thing forever or for a long time into the future. Hypergoogology's development is always unpredictable, we can clearly see that no matter how strange or big or complex something is, we still manage to find something bigger/better than it.

An example of this is "X is probably going to be the biggest thing we'll ever do, it's basically impossible to surpass in a major way without any naive extensions".
Reduk

Reduk is a number that ends up transcending a current standard for concepts that create large numbers, collapsification. Most top concepts currently focus on having to be automatically collapsed to a lower level for being so powerful, as an example being beyond English requires collapsification to English. Though this also introduces a new, rather novel concept to counteract other methods of simply beating the number.

## Auto-Collapse

The current meta for concepts is to have concepts so powerful that it's physically impossible to actually have them, and then collapse it to a possible level, notably LOT based numbers. It is without a doubt that there are certainly other ideas, possibly incredibly more powerful, that haven't been nearly thought of yet. That's enough "garbage text" without anything useful though, so onto the definition. An auto-collapsing concept is simply a concept such that the definition written on the page will make it less powerful. This does include levels of thought since for it to be written it has to be thought about.

## Definition

##### "True" Definition

Reduk is simply defined as being beyond any number defined using an auto-collapsing concept.

##### Simple Surpassion Counteraction

Since I hate it when there's just another concept created that is "on a new level" and thus invalidates my number's definition (looking at you levels of thought), I have come up with a method of counteracting simple countermeasures against good definitions (only half joking)! For any notion that takes in a number and gives other notions using a higher number more power, apply at the highest level not requiring collapsification. This includes everything since all notions boosting the power of other notions can be rewritten as a comparison of numbers.
Google搜索

**Google搜尋**是由Google公司推出的一个互聯網搜索引擎，它是互聯網上最大、影响最广泛的搜索引擎。Google每日通过不同的服務，處理来自世界各地超過30億次的查詢。

除了搜尋網頁外，Google亦提供搜尋圖像、新聞組、新聞網頁、地圖、影片的服務。2005年6月，Google已儲存超過80億個網頁，1億3千萬張圖片，以及超過1億的新聞組訊息 - 總計大概10億4千萬個項目。它也缓存了编入索引中的绝大多数网页的内容。

2016年3月11日，泰国Google更换了以《玛尼和她的朋友们》为主题的Logo以示纪念作者拉差尼·西派万的86周年冥诞。

## 参考资料

Template:Reflist

1. ↑ Google Doodle详情页面
The Law of Transposition

The Law of Transposition is the generalization of current hypergoogological methods to go "higher" than would otherwise be possible. However, before I explain how that works, we need to define a few things.

* The "state" of a number. A "state" simply means the set of every statement that a given object operates under. "Statement" is not an object itself, and is therefore not implied to be recursible in any way,although states themselves are recursive and can be stacked on eachother indefinitely, because a state also has statements it operates under, and therefore a higher "state" ruling it and many more different copies of it under the same rules. A higher state of an object y can be denoted as Syx+1, with the current state noted as Syx.
* Statements. A statement is any idea that would give us information about how an object would act when interacting with another object that also falls under said statement. (mostly seen as axioms.)

The Law of Transposition implies that for any given object x, exists an endless chain of states both higher and lower than its current state with an identical object x. (∀x (Sxn -> Sxn+1 )) This also explains naive extensions as just recursions of the current state of a number, but that's a topic for another post.

To not have naive extensions itself, all of them will be discussed in CIG.
Counter-Strength

Counter-Strength is a level 2 collapse of 'definition strength'.

Counter-Strength (CS) can be thought of as how 'strong' a definition is, it determines which definition is prioritised. A definition with CS n+1 will be prioritised over a conflicting definition with CS n or below. For example, if a number A with a CS of 1 claims that it is bigger than all other numbers, and a number B with a CS of 2 claims that it is bigger than A, B would be greater than A. However if A had a CS of 2 and B had a CS of 1, B would be greater than A. If both B and A had an equal CS, it can be assumed that they would be equal.
Conceptual Breaking Point (Ͷ)

Conceptual Breaking Point, **Ͷ** or CBP is a number defined in an attempt to beat PIL+ in a novel way that doesn't rely on thought levels.

## Hypersystems

Hypersystems are collections of concepts, each hypersystem has a specific number assigned to it, starting from level 0. Hypersystem 0 contains every concept definable and every concept discoverable to us, this would include concepts like thought levels (although paradoxically this definition is still on a thought level), hypersystems, hypergoogology.... ect. From here on, we can say that for n≥0, the contents of the n+1th hypersystem would be impossible to describe using concepts from the nth hypersystem. The n+1th hypersystem would also contain all concepts from the nth hypersystem too. This definition is written beyond any thought level but collapsed to level 2 by necessity.

## Definition

We can now say, for any given hypersystem, the contents of that hypersystem would not be adequate to describe the size of **Ͷ**, due to how large it is.
玛尼和她的朋友们

《**玛尼和她的朋友们**》（泰语：มานะ มานี ปิติ ชูใจ）是一部泰国1到6年级小学的泰语课本，共12冊。1978年至1994年由泰国作家拉差尼·西派万所作，迪炎·差春蓬负责插图。该书的主角为玛尼、玛纳、比迪和楚哉。

该作品自三年级册开始，内容偏向于神话及历史故事，逐渐少以玛尼作为故事主角。2014年4月29日，《玛尼和她的朋友们》发行了重制版，只是重绘插图，内容与老版相同。

简介
--

《玛尼和她的朋友们》的一年级册内容共40课。一年级册和二年级册插图是清新的水彩画风，内容也简洁易读。自三年级册开始，画风从原来的水彩清新插图变成阴森的黑绿双色插图，内容逐渐不再以玛尼作为故事主角，取而代之是泰国历史和一些神话传说。

该作品以一个安静美丽的村庄为背景，是泰国教育部出版的第五套教科书。
与其他泰国教科书不同的是，《玛尼和她的朋友们》是一部有故事背景、人设具体的教科书。

参考
--

1. ↑ 一起来围观泰国小学生课本. Retrieved on 7月 30, 2017.
2. ↑ รวมแบบเรียนชุดที่ 5 หนังสือเรียนภาษาไทยชั้นประถม ชุด มานี มานะ.
3. ↑ 抢先看！2014新版《玛尼和她的朋友们》.
4. ↑ 目前《玛尼和她的朋友们》在大部分泰语学习网站里多为一年级册内容，为广泛流传的版本。沪江泰语有二年级册的翻译版。
5. ↑ 泰国一共有6套教科书，你都知道吗？
Overition (o*)

Overition (o\*) is a part of the star series, the biggest number in the series.

## Logic Within Hypergoogology

So within Hypergoogology, we don't follow any normal logic. The logic within Hypergoogology is far more meta, complex and confusing. There seems to be 2 spheres of logic within Hypergoogology, one being individual logic and one being universal logic. For the sake of this page I will use the symbol [i\*] for individual logic and the symbol [u\*] for universal logic.

## Individual Logic

Each definition within Hypergoogology follows its own [i\*], we can number these; the [i\*] for the definition x is shown as [i\*/x]. So, what is [i\*]?

For the definition x, [i\*/x] is the laws of reasoning that govern x, these laws may or may not line up with standard logic. For example, if we define a number A such that it is "beyond all other numbers". However, we can define a new number B such that it is "beyond A". [i\*/A] and [i\*/B] contradict eachother here, within [i\*/A] it can be said to be true that A>B, but within [i\*/B] it can be said to be true that B>A. A number's [i\*] can be seen as its own "logical bubble".

## Universal Logic

[u\*] is the laws of reasoning that govern Hypergoogology as a whole. [u\*] governs all [i\*]... which means that [u\*] must decide which [i\*] are "more true".

Let's take the conflicting numbers A and B from above. Both A and B exist within [u\*] but we we have to find out which one to prioritise. To find out which [i\*]s we prioritise over other [i\*]s, we can use a thing called "definition strength", which for the sake of brevity I will show as [d\*], and the [d\*] of an [i\*] I will show as [d\*]->[i\*].

[d\*]->[i\*/x] is how many statements/axioms x gives for [i\*/x] to be prioritised or shown to be more true over other [i\*] within [u\*]. A and B are equal within [u\*] as [d\*]->[i\*/A]=[d\*]->[i\*/B] because their only statements conflict, A claims to be >B and B claims to be >A... this puts [i\*/A] and [i\*/B] in a strange form of equilibrium. However, let's introduce a new definition into the mix; C is defined as "C>A and it ignores [i\*/A]". Within [i\*/A], A>C, but within [u\*], C>A meaning that in Hypergoogology we would say that C>A. The reason that C>A within [u\*] is because [d\*]->[i\*/C]>[d\*]->[i\*/A] because C makes more statements against A than A does against C; A claims to be greater than C but C does not only claim to be greater than A, it also claims to ignore whatever A has to say.

## Definition

* [i\*/o\*] is defined such that for all n, o\*>n within [i\*/n].
* [i\*/o\*] is defined such that for all n, o\*>n within [u\*].
* [i\*/o\*] is defined such that for all n, [d\*]->[i\*/o\*]>[d\*]->[i\*/n].
* It is an axiom within [i\*/o\*] that the above and this statement itself must be true within [u\*].
Complete Xepition (cX*)

Complete Xepition (cX\*) is the larger counterpart to Xepition (x\*), this number uses many ideas from Xepition so please read that first.

## n-Ineffable

n-Ineffability is a way to describe different levels of ineffability. 0-Ineffable is the standard 1-Physical interpretation of the word. 1-Ineffable is so ineffable that it surpasses any form of n-Physics, its ineffability cannot be described, in any sense of "describe" at all. From then on, the n+1-Ineffable is to n-Ineffable as n-Ineffable is to n-1-Ineffable. This leaves us with things like "ω-Ineffable", and "Ω-Ineffable", even "x\*-ineffable" or "cX\*-ineffable"... even 1-Ineffable is so ineffable that we cannot even describe how ineffable it is (and even that is an understatement).

## n-Fysiks

n-Fysiks is an extension to n-Physics. It starts at 0-Fysiks, which contains all n-Physics. From then on, n+1-Fysiks is n+1-Ineffable to n-Fysiks.

## Definition

* **cX\* transcends all forms of n-Fysiks, regardless of any other definition.**
* **cX\* cannot be defined in any form of n-Fysiks, regardless of any other definition.**
* **cX\* cannot be described in any way in any form on n-Fysiks, regardless of any other definition.**
* **cX\* ignores anything that hinders its size or definition, even those that transcend "anything".**

## Note

cX\* is beyond Reduk despite using auto-collapsing concepts because:

1. The definition strength of cX\*.
2. For Reduk to surpass cX\* it must be either beyond all n-Fysiks, "beyond all n-Fysiks" or beyond "beyond all n-Fysiks".
The Loneliest Number (TLN)

TLN is a number defined to surpass s\*. It is still smaller than c\*.

## Definition

With the definition of "thing" defined in s\*:

TLN is the first number after nothing that has no relation to anything including itself, regardless of any other definition that claims to have a relation to TLN and it ignores anything that hinders its size or definition.

## General Weirdness...

TLN would have some strange implications. For example, TLN would not be greater or smaller than any other number, while still being greater and smaller than other numbers... It also means that TLN is neither greater, lesser or equal to itself. It wouldn't even be itself.... it isn't even different to itself. So, TLN is not TLN and its not not TLN at the same time. TLN cannot be considered a number while still actually being a number either, it's still a number but it "isn't" at the same time.
Kung Fu Panda 4 (2024 film)

***Kung Fu Panda 4*** is an 2024 upcoming American-Chinese computer-animated comedy action wuxia arts martial crossover film, it is the fourth installment in the Kung Fu Panda Franchise and the sequel to 2016's Kung Fu Panda 3, produced by DreamWorks Animation and distributed by Universal Pictures.

## Voice Cast

* Jack Black as Po
* Dustin Hoffman as Shifu
* Bryan Cranston as Li Shan
* Angelina Jolie as Tigress
* Jackie Chan as Monkey
* Seth Rogen as Mantis
* Lucy Liu as Viper
* David Cross as Crane
* James Hong as Mr. Ping
* Katy Perry as Mei Mei (replacing Kate Hudson)
* Ian McShane as Tai Lung
* Gary Oldman as Lord Shen
* J. K. Simmons as General Kai
* Victor Garber as Master Thundering Rhino
* Jean-Claude Van Damme as Master Croc
* Dennis Haysbert as Master Storming Ox
* Sam Rockwell as Mr. Wolf
* Zazie Beetz as Diane Foxington / The Crimson Paw
* Marc Maron as Mr. Snake
* Craig Robinson as Mr. Shark
* Anthony Ramos as Mr. Piranha
* Awkwafina as Ms. Tarantula
* Richard Ayoade as Professor Rupert Marmalade IV
* Alec Baldwin as Theodore Lindsey "Ted" Templeton Jr. / The Boss Baby
* James Marsden as Tim Templeton
* Amy Sedaris as Tina Templeton, Mr. Piranha's love interest.

## Trailer music

### Songs from the trailers and TV Spots

* Boyfriend - Justin Bieber (Teaser trailer; Official Trailer and TV Spots)

## Release Date

* March 8th, 2024 in the (United States of America)
* March 7th, 2024 in (Mexico, Colombia, Peru, Chile, Argentina and Brazil)

## Songs

* Kung Fu Fighting: performed by Jonas Brothers (new song)
*Θe

Zeinyt (\*Θe) is a zeroid, which is, put simply, a number less than all positives, yet greater than all negatives.

## Definition

(A1) For every non-empty collection of objects, **\*Θe** is either the unique least member of that collection, or there exists an object larger than **\*Θe** that is smaller than every member of the collection.

(A2) **\*Θe** is the only object with the unique property of being **\***signed. Being **\***signed is neither being positive, nor negative, nor any complex angle, nor signless, nor any other kind of sign (such as hyperpositive, hypernegative, etc.) other than itself.

## Consequences

From it's definitions follow many consequences:

Firstly take the collection of all reciprocals. Either **\*Θe** is in the collection or it is not. If it is, then it is the reciprocal of some fictional infinity. **\*Θe** is the strictly least member of the set, which means it's reciprocal must be the largest possible fictional infinity. There is no largest fictional infinity however, therefore **\*Θe** can not be in the set of all reciprocals. Therefore there must be a larger object than **\*Θe** which is not the reciprocal of anything. It follows that **\*Θe** can also not be the reciprocal of anything. Therefore:

Because **\*Θe** is **\***signed the product of **\*Θe** with any other number must be **\***signed as well. Since it is unique in this sign, the product must be **\*Θe**.

Furthermore

**Э** x **\*Θe** = **\*Θe**

Without contradiction to **Э** (Conkept). This is because this must be true of all numbers, so Conkept has smaller objects with this property, namely anything.

**\*Θe** is believed to be remote. This means that for any interval (**\*Θe**,x), there can be any infinity number of objects strictly between them.
Quandale Dingle's Array Notation

Quandale Dingle's Array Notation is a "goofy ahh" array notation created by Icosalord. It can generate numbers in Tier 1.

## Linear QDAN "fart sound effects"

Rule 1: Chop off all 0's at the end

Rule 2: For all arrays longer than 1 entry, if the array has any entry higher than another array's entry at that spot, it is larger, as long as the other array does not have a larger entry after that entry, in which case it is larger.

Rule 3: For 1 entry arrays, they are equal to their first entry.

## Dimensional QDAN "finally we can afford dimensions"

Rule 4: If the array has a dimension indicator of (a)array at the end or after another dimension, it is larger than all arrays with (a)smaller array according to Linear QDAN, and all arrays with (a-1)any array at the end. a>=0

Rule 5: If a is an array, it is defined by Rule 2 of Linear Notation, but for arrays with the array within dimensions.
Diaeresis (🞜)

Diaeresis is Icosalord's second number attempting to be within Tier 5, although it lands in tier 6. with the help of GOODELS to refine the idea within the definition.

## Definition

* Diaeresis transcends being able to have any statements apply to it, regardless of what statement is or if it cannot be considered a statement, no matter what any other thing says.
* It ignores anything that hinders its definition or size.
The One True Door (S3)

Artistic Representation of the Door

### Basic Information

The One True Door is the god worshipped by the Dorian people and people who practice Dorianism. All of these people come from the Fallen Empire of Great Doria.

*You may be looking for the One True Door from EarthCraft Season One.*

### History

The One True Door is the creator of the universe and all of doorkind. It created all humans and doors, however, humans have enslaved the door and forced them to act as entrances with no payment. This is what Dorians and all of the people from FEGD aim to stop.
Complete Surpition (cS*)

Complete Surpition (cS\*) is the bigger counterpart to Surpition (s\*). It serves as an end to a portion of Hypergoogology, as to beat it we will need some new ideas to surpass it.

## Definition

* Nothing cannot be considered a "thing", including those that are not things, and those that exist outside "nothing", regardless of anything in their definition to counteract this.
* All things, including cS\* are smaller than cS\*, regardless of anything in their definition to counteract this, including those that lie outside "anything".
* c\* simply ignores anything that may hinder its size or definition.

## So... what next?

It might seem that cS\* is the end... but we can always go beyond. In Hypergoogology we always find some sort of way to go beyond, even with the thickest of walls. I'm not quite sure what to do after this but we certainly can. Absolute Infinity was once a brick wall, SFP was once a brick wall, and PIL+ was once a brick wall, but we still found ways past these. I encourage anyone reading this to start thinking about what we could do to go beyond this.
List of Hypergoogological Numbers

## Tier 0 (-) (Zeroids)

* [intentionally left blank]
* True Absence
* \*Θe
* Sub-Zero
* Absence
* 0
* Almost
* Something?

## Tier I (ᛜ)

* Contrology
* Absolute Everything
* Protology
* The Successor Fixed Point
* 𐆓0
* Limit of Linear QDAN
* Limit of Dimensional QDAN
* 𐆓-MAX

## Tier II (ᛃ)

* Outerconst
* Postfinity (∰)
* Posterfinity (∰+)
* Subition (s-)
* Conkept
* Complete Subition (cS-)
* ∀-

## Tier III (ᛡ)

* Multission
* Catafinity
* Weak Omnicollapse
* PIL+
* Onte-Cancipt
* Conceptual Breaking Point (Ͷ)

## Tier IV (ᛟ)

* Opsib-Ranot
* Anadromic Limit
* Perfect Conkept
* Xubition (x-)
* Limits Limit (LL)
* Obama's Number
* Limits Limit+ (LL+)
* Dedication (ණ)
* Hyperconkept (Э+)

## Tier V (ᚷ)

* Complete Xubition (cX-)
* Surpition (s\*)
* The Lonliest Number
* Complete Surpition (cS\*)
* Reduk
* Diaeresis (🞜)
* Xepition (x\*)
* Complete Xepition (cX\*)

## Tier VI (△)

* Overition (o\*)
* Pseudo Finality (p.F)
* Modity (MP)
* Fairly Sizeable Number (⅋^)
* Beatable+ (ҍ!)
* Lirem
* Meaningless+ (m!)
* Interpretable+ (i!)

## Tier VII (◈)

* Opux (!!)
* Perfect Catafinity (♔)
* Full Opux (!!!)
* Unitude
* Exofinity (◉)
* Multitude

## Tier VIII (✦)

Metatude

hypertude

## Tier IX (∞)

Verses

Bengalfinity

## Tier X (Ω)

back to 0 again and again for infinity times

Benny maths
Multission

If this definition works as I intend, it's probably pretty big, if not, oh well. Since I sort of dislike "ignores other things", I didn't add anything along those lines, and thus this is likely smaller than s\*, though it is larger than the minus versions of these.

## Definition

Consider all possible universes (every combination of particles and whatnot), call all of these possible universes U. For all numbers v defined within a universe in U, Multission surpasses v.

Of course, Multission must surpass itself since our universe is in U, but that isn't a problem because hypergoogology. It is debatable whether it is larger than things with ignorance, since ignorance can be used in the other universes, but ignorance just says to stfu about that.
Posterfinity (∰+)

Posterfinity (∰+) is an extension of Postfinity (which itself is an extension of Outerconst).

## μ-types

1. All μ-types can have their own set of axioms.
2. The first μ-type is the set of all Mn, Mn is defined within the Postfinity definition.
3. The limit of the n+1th μ-type must be larger than the limit of the nth μ-type.
4. The axioms that are needed to describe the n+1th μ-type must be fundamentally inconsistent with the axioms that are needed to describe the nth μ-type.
5. The n+1th μ-type must be able to describe all numbers contained within the the nth μ-type.

## The μ-set

The μ-set is the set of all limits of every μ-type. This set cannot be described in any μ-type.

## Definition

Posterfinity is now defined as the first number such that is is beyond any member of the μ-set.
Hypothetical Numbers

Hypothetical numbers are numbers that are.... well, hypothetical. They could never be truly defined by us because by definition they cannot be defined. These are not truly numbers because they are completely undefined, they're just ideas of numbers. They are not fictional numbers like what you might find in fictional googology, they are just vague ideas of things beyond our wildest imaginations.

List of Hypothetical (undefined) Numbers
Thought Levels

Thought levels, originally defined by serge, are an extremely powerful concept within hypergoogology.

## Definition

Each thought level has a number, starting at level 0 and extending onwards forever. Each level is a level of definition that a certain concept can exist on. A statement written in level n+1 has the ability to control a reality beyond the true comprehension of an entity living in the reality controlled by level n. We are thought to exist on level 3, level 0 being pure concepts, level 1 being the level that can describe level 0, level 2 describes level 1, and level 3 is thought to be the reality that we exist in, which we can describe level 2 on.

## Example

For example, a concept on level 0 saying "this concept will break through your screen" wouldn't break through your screen, and it wouldn't make sense because of the fact it doesn't actually break through your screen. a concept on level 1 saying "this concept will break through your screen" wouldn't break through your screen, it is just the concept of a message breaking through your screen. A concept on level 2 saying "this concept will break through your screen" wouldn't break through your screen, it is the concept of a message actually physically breaking through your screen. It would be impossible for us to describe the concept of "this concept will break through your screen" on level 3, as it would literally need to break through your screen to count as actually happening on level 3.

## Level Collapse

Levels of thought can be "collapsed" downward. We could take a level 2 concept and collapse it down to level 1 for example. Let's take the idea of "this concept will break through your screen" from before, if we imagine the idea of this concept existing on level 3 but the concept exists on level 2, then we are collapsing the concept from level 3 down to level 2. We could collapse a level 4 concept down to level 2 by saying "the concept of this concept breaking through the screen on level 4", by creating this concept, it automatically exists on level 2 since it would be impossible for us to access level 4, therefore we have just collapsed a level 4 statement down to level 2.
Obama's Number ( ҈ )

Obama's Number is a number created by Icosalord in an attempt to surpass the Anadromic Limit.

## Absolute Concepts

Absolute Concepts are beyond all concepts, all of their properties are absolute, and they can't be put into a set. Anything based on them will inherit these properties.

## Limit Tiers

For this we use the definition of Limit in Limits Limit (Lᴸ).

The Anadromic Limit would be considered L1, the limit of Absolute Concepts is L2...

Ln is the limit of any bypass that bypasses L(n-1).

At the Ln fixed point, define LL1 as the limit to any way to bypass it. Then you can add 1 repeatedly defined the same way as Ln. The limit of that is LL2, and L^a(b) is defined as L^a(b) being beyond all L^a-1(c), no matter the c. L^a(b) is also beyond all L^a(b>), and LL1 is L^2(1), LL2 is L^2(2), and so on.

## The Definition

Obama's Number is the final limit of all L-recursion and recursion in general, no matter the bypass used or anything else. For obvious reasons everything in the definition has been collapsed to Thought Level 2.
Beatable+ (ҍ!)

Beatable+ (ҍ!) is a tier VI number.

## Definition-Transcendentalism

When a definition is made within Hypergoogology, we assume it follows all of the rules and definitions and assumptions of Hypergoogology. Some of these rules/assumptions and definitions are what "numbers" are, what definitions can and can't do, how we compare definitions and so on. I will call these Hypergoogological assumptions (HA). But what if something simply ignored HA? What about a definition that completely follows its own logic regardless of what HA say about it being "only individual logic". I will call definitions that are whatever they want to be regardless of any other system's assumptions (specifically HA) "transcendental definitions" (TD). To take a TD and put it under HA would be to fundamentally change it's entire meaning and definition.

## Definition

ҍ! is the largest number, simply because it wants to be so, it's a TD and it simply does not care if Hypergoogology agrees with it, because to take ҍ! and put it under Hypergoogology while keeping the entire definition completely in-tact would be simply impossible. ҍ! is the equivalent of giving up on HG and realising that you'd be happier if your number was automatically bigger than anything in your own mind. ҍ!, in it's own mind is simply beyond Hypergoogology and it realises that if it thinks it's the largest number, it is.

## Further Explanation

When you see this for the first time, you might be thinking "what? so we just surpassed Hypergoogology?"... and, well no, ҍ! still exists within Hypergoogology. It's definition is still just it's own individual logic. To say this number is actually beyond Hypergoogology is the Individualism Fallacy. At this point, definitions are so "fucked up" that they can mean completely different things from what they say. Take "this number is beyond all definition" for an example, this number is valid in Hypergoogology but it isn't *actually* beyond all definition.
Absolute Infinity

Absolute infinity is a paradoxically huge number, unaccepted by regular mathematics.

## Cantor's Absolute Infinity

Cantor's absolute infinity is defined as the system of all ordinal numbers.

### Burali-Forti paradox

If Cantor's absolute infinity, Ω, were consistent, as a well ordered set, a number, n, would exist that is greater than all numbers in Ω, yet n would have to be contained within Ω since Ω contains all numbers, implying that n>n, which is a contradiction. Therefore *The system Ω of all [ordinal] numbers is an inconsistent, absolutely infinite multiplicity.*
Absence

An "Absence" is something that will never be thought of, thus not having a name, a symbol, a definition, rendering it totally and utterly inexistent to the existential axiom. Its "bigger" counterpart is Undefined, which is something that isn't yet thought of, but inevitably will be, rendering it inexistent only for a certain amount of time.
Modity (MP)

Modity is a number similar to Beatable+ (ҍ!), although it is currently undecided which is larger. Modity was made after noticing a trend used by the largest numbers at the time, although it was a lot longer before EIG decided to actually write about it (lazy smh).

## Models

Call a model of hypergoogology a model that aims to solve the problem of contradictions in definitions. For example some hg models are u\* and software bribery, although both act similarly in that there are two parts the "truth", and what each definition "wants", there are likely many undiscovered hg models that do not act this way. This means that there is likely a "super-model", it is a hg model that to determine the "truth" looks through every other hg model, and chooses the most common outcome for each of the models to determine a relation between numbers. This super-model, however, is actually very weak as all models have an inverse model, so in it, everything would be equivalent. By inverse model, I mean a model which has the opposite opinions on where each number lies in relation to each other.

## Definition

Primitive Modity (PMP) is defined as a number such that for all models of hg M, it is defined as PMP>N for all N with the highest strength possible in M.

Weak Modity (WMP) is defined as a number such that for any particular model of hg M, WMP exists beyond of the jurisdiction of M. (similarly defined to Perfect Conkept)

Reduced Modity (RMP) is defined as PMP with the definition of model altered to include anything that claims any relations to any numbers.

Modity (MP) is defined as WMP with the definition of model altered to include anything that claims any relations about any numbers.
Party Dynamics

Deciding ahead of time why your party, or at least parts of your party, have found the road together, can be a great way to give the party some ground to go off of as they leave for their adventures.  You could make your characters related to one another, you could make them all from the same town, or you could all make them frequents of the same bar.  Below are some more official options, patronages that can drive motivations of the story forward and allow characters to explore new places.  If you think your group might benefit from a patron, take a look at these:

The Academy:  a school funds your pursuits

The Ancient One: You all serve the same divine being

Aristocrat: You all serve a wealthy noble

Crime Syndicate: You all work for an underground network

Guild:  You all help protect or errand for some kind of artisan’s guild.

Military Force: You all serve or served together

Religious Order: You serve the same group of divine officials.

Sovereign: You serve a ruler

Adventurer’s Guild: Monster Hunting IS the business

Espionage/Detective Agency:  Stealth and information are your goals

Newspaper: You are there for the drama, the meat, the stories.
OTN

OTN is a language for creating properties and combining them to create super huge numbers.

## Definition

##### Variables

* Let Ex for any x denote a valid OTN expression
* Let Nx for any x denote a number
* Let Px for any x denote a property

##### Rules

* ∃

N
x

(

P
x

(

N
x

)
)

{\displaystyle \exist N\_x(P\_x(N\_x))}

 Means Nx has Px
* ∃
l

N
x

(

P
x

(

N
x

)
)

{\displaystyle \exist\_l N\_x(P\_x(N\_x))}

Means Nx is the least number with Px
* ∃
g

N
x

(

P
x

(

N
x

)
)

{\displaystyle \exist\_g N\_x(P\_x(N\_x))}

Means Nx is the greatest number with Px
* ¬

P
i

(

N
j

)

{\displaystyle \neg P\_i(N\_j)}

Means

P
(

N
j

)

{\displaystyle P(N\_j)}

is false
* P
i

(

N
j

)
∧

P
l

(

N
k

)

{\displaystyle P\_i(N\_j) \and P\_l(N\_k)}

Means both

P
i

(

N
j

)

{\displaystyle P\_i(N\_j)}

and

P
l

(

N
k

)

{\displaystyle P\_l(N\_k)}

are true
* P
∀

{\displaystyle P\_\forall}

Means any property

##### Builtin Properties

Builtins

P
i

<

N
j

{\displaystyle P\_i < N\_j}

N
j

=
0

{\displaystyle N\_j = 0}

N
j

=
s
(

N
i

)

{\displaystyle N\_j = s(N\_i)}

∈
(

N
j

)

{\displaystyle \in(N\_j)}

N
j

>

N
i

{\displaystyle N\_j > N\_i}

This is by no means meant to be a constant language, if you want, feel free to add new builtins.

## Examples

Examples

∃

x
j

(
¬
(

∃
l

x
i

(

P
∀

(

x
i

)
)
∧

x
i

>

x
j

)
)

{\displaystyle \exist x\_j(\neg (\exist\_l x\_i(P\_\forall (x\_i))\and x\_i>x\_j))}
Birth Chart

There are Ten Months, divided into two seasons (Loxos and Hamori).  Each month is 35 days long with 7 day weeks.  The Days of the weeks are:

Wickstei, Shaktei, Runstei, Fraltei, Lentei, Arcostei, Graztei

Pick a month to be born during, and even a day if you would like.  Each month has an associated goddess, Vitali or one of her daughters.  The goddess you are born under has effects that you will discover through roleplay.  Each month also has a major holiday to give you some flavor.

### The Season of Hamori

Dustgaze (Zariel)

12: Burnleaf - Zugtov’s holiday of decay and death

Stillward (Keros)

30: The Blaze, Keros’ holiday of warmth and winter tidings

Windbone (Ezra)

14: Solace, Frondar’s holiday of preparation for winter

Gloomstalk (The Raven Queen)

5: Spinnersleep - Vitali’s Holiday of hibernation and sleep

Longthaw (Avandra)

35: Embertide - Redona’s Holiday

### The Season of Loxos

Dovesong (Millil)

23: Ascension - Auzenar’s Holiday of rebirth. A celebraation of civilization and the arts, this holiday typically involves music, markets, and festivities.

Petrichor (Sehanine)

18: Midsommar - Faesi’s Festival of new birth, sprouting and sowing. Plants, weed, fresh food and ceremonial dance are intrinsic to this holiday.

Heatsink (Lolth)

30: Highsummer - Lolth’s celebration of heat and dryness. This festival is not practicec everywhere, but sruidic ceremonies are often involved.

Silkbreeze (Vitali)

3: Hunter’s Rune - The rebirth of the world, the beginning of the hunt. This holiday typically involves a great hunting party, a celebration of ranging and freedom, a pilgrimage or a great feast.

Redsage (Arawai)

21: Wildharvest - Arawai’s festival of fertility
Erahled

The noises of an overcrowded inn suuround you. Clinking glasses, shouting patrons, discordant music, and the thumps, thuds, anc screams of the fighting pit below. You sit among the lofted tables which overlook the fighting pit, where a half ogre risks her life against a giant scorpion for coin. Lunging in her seat, a tabaxi with large hoop earrings keeps her eyes on the fight as she reminisces the glory days.

*We used to be legends. Back when things were clear, and it was us versus them in the open ocean, we were heroes. But now, since the Lich King and the Pseran Empire fell, the empires act like we never even existed. So, fuck ‘em, we said, we’ll make our own way. The Sapphire Sea is our home now, and both empires be fucked. The men I almost drowned are my kin, and the people who paid me to do it hunt us like animals. That’s the pirate’s life, kid. Not as many bells and whistles as ye thought, huh? Well, what do ya say?*
Vitali's Web Wiki

# **A Spinner's Guide to Vitali's Web**

##### Homebrew Campaign Setting Info Wiki

Lore on the Web catered towards players and character creation. The Web is designed to foster player freedom and a sense of place. It is a place of fantasy, mystery, science fiction, witchcraft, magic and powerful secrets. It takes much of my own writing and combines it with 5e as well as my many influences and resources, a few worlds that have collided with my own being those of Nintendo's Hyrule, Stephen King's Mid-World, Matthew Mercer's Exandria setting, Pendleton Ward's Ooo, the futuristic empire of Frank Herbert's Dune, and The Book of the New Sun. Click below to get started exploring, or check out the Character Creation and Lore Introduction pages, or head straight over to Game Select.

Art, locations, characters and concepts that may be familiar to some users and are found in this wiki are borrowed for the purpose of immersion and will not be used for profit anytime soon or without permission.

## Important articles

The Greater WebXarn'ItorThe Free City of AtankaLanesseSigil

* Rules of this wiki
* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles
* Fitting in to the Party
* Game Select

You can also be part of the larger Fandom family of communities. Visit Fandom's Community Central!

*Community Founders*: Write a good and paragraph-length description for your welcome section about your topic. Let your readers know what your topic is about and add some general information about it. Then you should visit the admin dashboard for more tips.
Post-Undefinable (PU)

PU is an Undefinable number, meaning that it has no true definition because it would be impossible for us to define. It is a hypothetical number and not an actual one.

## """Definition"""

PU is a number that could never be defined, at all. It is too big for any definition that could ever exist regardless of thought level or anything else. It is *truly* ineffable in every sense, it is a concept that could never exist within any hypercosmological space, it could not even exist as an abstract concept. It is beyond any form of anything.
Kaitan

The Dunewalker’s meeting hall is lined with strange stones, hookas, and hides of many strange beasts. A sandworm with a three-pronged jaw, the serpentine eye of a tarrasque and the screaming head of a glabrezu are noteworthy,. A carrion crawler’s radiant exoskeleton serves as the chandelier of this parlor. A giff (hippo humanoid) lets out a long exhale of hookah smoke. Barely keeping you in thier vision, they continue their story.

*Some say we never would have pushed back the demons without the alchemists. Some say it was the trancers, and still many claim that the. warforged of Ludendorf are the only might that really mattered. I say they’re all full of shit. The rifts are sealed and the world is new, and thats all that matters. It’s a new age, and we might be starving along with the land, but if we can get our shit together and stop all this petty raiding and little bullshit, we might be able to rebuild what Laverndan once was, maybe even get ourselves off this shithole again.*