recursal/Fanatic-Fandom huggingface dataset:
The Downfall Documentation Wiki

### Welcome to the Downfall Documentation!

A Wiki containing all Outskirts related info, from plants and animals to planes and locations.

To get in touch with the Outskirts community consider joining the Discord Server and check out my DevianArt (currently inactive) account where i post lots of Outskirts art! Here is also my YouTube channel which contains many update videos with SimplePlanes tracing models for various planes that appear in the series.

### What is Outskirts?

Outskirts is a collective universe for several bits of media that i (F-32) am working on with the help of the community.

The universe of Outskirts is separate from our own: A cascading series of events in world war 1 and 2 caused the earth to be turn slightly dystopian and geologically unstable, where a massive fracture spanning across central Europe creates several interesting ecosystems filled with culture and wildlife. Through the different stories in Outskirts a lot of interesting technological advancements can be seen that vary from the ones in our world.

#### The current projects within the Outskirts universe are:

The Sunken Quarter Series (main story of Outskirts)

* Upper Limiter
* The Outskirts
* Shadow of the Cloudbreacher
* Low Divide (The Remainder)

Far Before the Fade (FBtF)

The Lingering Memories of Yakov Dryagin

Wire Fortress

*Need help building out this community?*

* Rules of this wiki
* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles

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.
Attackers

Attackers, also known as strike aircraft are Aircraft designed for ground attack, anti ship, anti airmarine and air strike roles among others. They are most often well armoured and built around carrying more payload in trade for the agility needed for air to air combat.

Dw5 "Waver"

Ship Eater

Rigband Accelerado
Groundlock

A groundlock is a rapid change in air pressure above the main wing of a canard or tri-wing plane. It is caused when the ground effect deflects airflow from a canard or moustache downwards and back upwards over the main wing thus pushing the affected plane down.

A groundlock occurs most often at high speeds and at around 3 - 10 meters above ground. While a plane is in a groundlock it's ability to pitch up is partly hindered and it's altitude may dangerously drop. A known trait of a groundlock is that it is exited very rapidly which often causes planes to aggresively ascend for a short period of time.

As a plane is able to enter a groundlock even while flying along a non-horizontal surface airmarine attack aircraft are known to often enter them while doing closeby strafes.
Ironcloud

Ironclouds are a species of snails that live all across the world as they travel by wind. they are tiny and have such small shells that they look like grits of sand when looked at in large numbers. They feed on algae in the air and are kept together due to the slightly magnetical properties they have. This is due to their shells being made of iron. Rains that fall from ironclouds are usually tinted red from rust and when a large ammount of ironclouds stays near land they leave behind a rusted metalic smell.

Flying a fast vehicle through an ironclouds can damage most air-breathing engines and sandpapers-off paint as well as messing with finer or more fragile machinery. Dryer ironclouds can also grind against canopy glass making it hard to see through. Ironclouds also tend to be inconvenient as they act as fairly solid walls to most types of radio signals. their massive size makes this an extra big issue as sometimes long range communication between stationary points can only be achieved after waiting for days for an ironcloud to pass.

Ironclouds are often collected by massive magnets and smelted down on airmarines into rotsteel.
Outskirts (cliffs)

The Outskirts are massive tectonic plate walls surrounding the entirety of the downfall. In height they span between 6100 and 6700 meters and are exponentially smoother the higher they go as all their plateaus are located at lower altitudes. Certain higher plateaus that failed to collapse when the downfall was quarantined were destroyed by the Surface via various artillery.

The base of the Outskirts lowers down into the Afterfade while the top reaches above sea level as it passes the moss ring.
Airwell

The Airwell is a massive cyclone of clouds that forms during most of January over the Sandbank in the Downfall. It is caused by the hot air of the sandbank escaping upwards and causing denser, cold air to rush in towards it. This continues for a whole month due to the eye acting as a light funnel focusing light towards sand that heats up and keeps the cycle going. Due to the nature of the Sandbank this process is continued until the surrounding air is warmed up enough to lower the temperature difference between the surrounding air and the air in the eye of the storm.

The temperatures needed for an Airwell to form are highly specific so cloudy weather has proven to be able to delay the formation of an Airwell for a pretty long time.

The eye of the Airwell is always calm with wind being consistent if even present. The ring of the Airwell itself is rarely that chaotic and is most dangerous on the ground as it can stir up lots of algae spore dust if the ground is dry enough.

The Airwell is necessary for the blooming process of the bleeding moon to be possible.

As of 1987 the eye of the Airwell is known to sometimes be used as a passage below the upper limiter by surface planes as the eye never contains any clouds making it easy to notice and avoid any potential ruin clouds that may have been previously deployed.
Decillion

*For Tiaokhiao's decillion, see nonillion.*

A **decillion** is equal to 1033 (America), or 1060 (France and Germany).

## Aliases

* Aarex Tiaokhiao - **Mecillion**
* Russ Rowlett - **Hendekillion**
* Username5243 - **Dekillion**

## Examples

* The area of the Milky Way galaxy is approximately 702 decillion square kilometers.
* The Sun weighs about 1.989 decillion grams.
* A decillion gallons of water would be 19 million km wide.
* A decillion dollars would be 200,000 km in diameter, a bit larger than Jupiter.
* A decillion atoms in a cube would be 13.4 meters wide, larger than most people's houses.
* SI Prefix: daka- (S)/nedaka- (L)
* SI Reciprocal Prefix: uco- (S)/enneco- (L)
Tarski-Grothendieck set theory

**Tarski-Grothendieck set theory** (TG) is an extension of ZFC formed by adding "Tarski's Axiom," which assures the existence of a "Grothendieck universe" for every set within the domain of TG.

## Tarski's Axiom

Tarski's axiom states that for every set A there is a "universal closure" set B for which the following holds:

* A is in B.
* Every element of every element in B is also in B. (B is transitive.)
* B is closed under pairing, powersetting, specification, and replacement. (Applying these axioms to any set within B gives us another set in B.)

B is called a universal closure and also a Grothendieck universe because B resembles the universe of all sets when one confines themselves to the axioms of ZFC and uses only elements of B as the domain of discourse. Due to vacuous truth, {} counts as a Grothendieck universe and because there is no requirement B be closed under Axiom of Infinity, the set of all finitely hereditarily definable sets (Vω) is also a Grothendieck universe. Past these, Grothendieck universes always have a strongly inaccessible number of elements.

## Use

The strongly inaccessible Grothendieck universes of TG can be used to model ZFC. TG is in turn modeled by VH where H is the first 1-inaccessible.

**Set theory**

**Theories**
Pocket set theory ★ Morse-Kelley set theory ★ Neumann-Gödel-Bernays set theory ★ **Tarski-Grothendieck set theory** ★ Zermelo-fraenkel set theory

**Axioms**
Axiom of Choice ★ Axiom of Extensionality ★ Axiom of Infinity ★ Axiom of Pairing ★ Axiom of Powerset ★ Axiom of Regularity ★ Axiom of Replacement ★ Axiom of Specification ★ Axiom of Union

**Objects**
Zero sharp ★ Von Neumann hierarchy

**Pioneers**
Abraham Fraenkel ★ Ernst Zermelo ★ George Cantor ★ John von Neumann ★ Kurt Gödel
Execution Dive

An execution dive is a last ditch maneuver that airmarine crews do in order to take down an enemy airmarine in the more survivable method then traditional ramming. An execution dive is performed by initiating an angled dive with an airmarine of a size/weight class similar to the enemy. The targeted airmarine is to be tethered via anchors before the airmarine preforming the dive passes below it. If enough vital points are tethered well enough the resulting force greatly damages the target while slowing down the diving airmarine.

One of the reasons why execution dives are effective is because the anchors are shot from a fast moving source twoards it's direction of travel causing the speeds to be added up increasing greatly the chance of successful anchoring.

Quartering is an effect that may occur during a high speed execution dive that had lots of tethers being fired at the target. Quartering is the act of the two airmarines being torn in half horizontally due to sudden decelleration caused by the tethers connecting them. Most of the time the diving airmarine is torn from front to back and vice versa for the victim of the dive.
Octillion

**Octillion** is equal to 1027 (S) or 1048 (L).

## Examples

* An octillion gallons of water in a sphere would be 190,000 km wide, comparable to Proxima Centauri.
* The Earth weighs about 5.98 octillion grams.
* The Sun weighs about 1.989 octillion tons.
* The volume of the Sun is about 1.412 octillion cubic meters.
* A tower of an octillion people would be 180 billion lightyears high.
* An octillion dollars would cover the world with a layer 15 km thick.
* An octillion atoms in a cube would be 13.4 cm wide, larger than many household items.
* The human body contains 7 octillion atoms.
* SI Prefix: xenna- (S)/pedaka- (L)
* SI Reciprocal Prefix: xono- (S)/penteco- (L)
Novemvigintillion

The **novemvigintillion** is equal to 1090 (S), or 10168 (L).

## Aliases

* Russ Rowlett - **Triacontillion** (not to be confused with triacontillion)
* Username5243 - **Enneicosillion** (not to be confused with enneicosillion)
* Aarex Tiaokhiao - **Noonagintol**, **90-noogol**
* Sbiis Saibian - **Googolspeck**

## Scale

* If the observable universe was 1 meter across, 1 novemvigintillion gallons of water would be the size of an oak tree.
* SI Prefix: icxena- (S)/peczeta- (L)
* SI Reciprocal Prefix: enneicoso- (S)/heptepentaconto- (L)
Quadrillion

**Quadrillion** is equal to 1015 (S), or 1024 (L).

## Full decimal form

* S: 1,000,000,000,000,000
* L: 1,000,000,000,000,000,000,000,000

## Examples

* It takes 210 years for Niagara Falls to use a quadrillion gallons of water.
* The Great Lakes have a volume of about 6 quadrillion.
* The Universe is about 473 quadrillion seconds old.
* The distance between one end of the Milky Way to another is about 586 quadrillion miles.
* A quadrillion words is about 11 billion books.
* A sphere of a quadrillion gallons of water is 19 km wide.
* A tower of a quadrillion people would reach 1.7 trillion km high, past the orbit of Pluto.
* A count to a quadrillion takes over 200 million years.
* A quadrillion seconds is about 31 million years, around the middle of the extinction of the dinosaurs and the human appearance.
	+ Quadrillion Minutes - 1.9 Billion Years
* SI Prefix: peta- (S)/yotta- (L)
* SI Reciprocal Prefix: femto- (S)/yocto- (L)

### Aliases

* ~~Donald Knuth~~ a random editor on faketest or ln wiki - **Femtiad**, **petund**, **lunion**
Land Cloud

Land Clouds are large puffball fungi that grow in the Downfall. They are extremely varied and due to the difficulty of categorising all their species they are seen as more of a gradient. They most commonly form uneven shapes with a tough rubbery surface. Depending on the soil and nutrients they are exposed to their colors may vary from the most common creme colored ones all the way to the artificially colored dark ones. Some common types of land clouds have a white, light brown or cyan patterns on their fruitbody.

Land clouds are not suitable for consumption but they aren't inedible either as they have been known to be used as famine food. They are fairly unique to most other fungi as when healthy they have a fairly small and non-connected mycelium that clusters at one point and connects to the fruitbody of the land cloud similarly as a root would form on a germinated seed.

At the end of it's life cycle the land cloud's mycelium rots away forcing the scilophen within it to lift the fruitbody to fly upwards the untill the pressure difference causes the land cloud to burst and spread it's spores in a large radius. The phase at which land clouds reach the end of their lifr cycle is when their furitbody becomes soft enough to be eaten by small invertebrates. This means the process can be delayed by feeding the land cloud many common natural pest repellants to cause it to be an unfavourable source of food for most critters.

Due to the high scilophen contents within the land cloud's segmented internal fruitbody and it's natural resilience it has become a required component for all living airmarines. In order for the land cloud not to starve it can be fed most compostable foods and many non-compostable foods that can be consumed by humans. For this reason land clouds are most often fed via specifically made solid ceramic or holed titanium pots called lift urns.

The other uses of land clouds in industry is scilophen and azure shriek.

A common profession in the Downfall is Land Cloud cultivation
8

**8 (eight)** is a positive integer following 7 and preceding 9.

## Properties

* 8 is the number of vertices in a cube.
* 1 byte is equal to 8 bits.
* It is also the number of directions most people choose from when specifying them on a map.

### In googology

* Latin Prefix: **octo-**
* Greek Prefix: **octa-**/**okto-**

### Aliases

* Faketest (Cloudy176) - **Bwo**
* Faketest (Username5243) - **Trwo**
Sexvigintillion

The **sexvigintillion** is equal to 1081 (S), or 10156 (L).

## Aliases

* Russ Rowlett - **Hepteicosillion** (not to be confused with hepteicosillion)
* Username5243 - **Hexeicosillion** (not to be confused with hexeicosillion)

## Scale

* 1 sexvigintillion gallons of water would be ~1.6% the size of the observable universe.
* SI Prefix: ikecta- (S)/pekena- (L)
* SI Reciprocal Prefix: hexeicoso- (S)/mepentaconto- (L)

## See also

* Unvigintillion
* Duovigintillion
* Trevigintillion
* Quattuorvigintillion
* Quinvigintillion
* **Sexvigintillion**
* Septenvigintillion
* Octovigintillion
* Novemvigintillion
Sextillion

**Sextillion** is equal to 1021 (S) or 1036 (L).

## Examples

* The Earth weighs about 5.98 sextillion tons.
* The ocean contains about 6 sextillion cups of water.
* The volume of the Earth is about 1.085 sextillion cubic meters.
* The distance between one end of the universe to another is about 87.9 sextillion miles.
* A count to a sextillion takes 200 trillion years.
* A sextillion seconds is about 31 trillion years.
* A sphere of a sextillion gallons of water is about 1900 km wide.
* A tower of a sextillion people would reach 180,000 lightyears high, larger than the diameter of the Milky Way.
* A sextillion atoms in a cube would be 1.34 millimeters wide, about the size of an average flea.
* SI Prefix: zetta- (S)/henda- (L)
* SI Reciprocal Prefix: zepto- (S)/meco- (L)

### Aliases

* Donald Knuth - **Zeptiad**, **zettund**, **jovion**
Guppytoll

The **guppytoll** is equal to 102000.

## Full decimal expansion

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000

A **thousand** is a number equal to 1000, or 103. The term came from Old English "|pusend", from Proto-Germanic "thusundi". A thousand is used as a base in the widely used -illion naming system, since all -illions are powers of a thousand. It is rarely called as **ten hundred**.

One thousand sheets of paper is called a **bundle**.

## Visualization

* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................

## Properties

* 1000 seconds is equal to 16.666667 minutes.
* It takes 8 hours for a faucet running at full power to waste 1000 gallons of water.
* Roman Numeral: **M**
* Ancient Egyptian Glyph: Lotus Plant

## In googology

* SI Prefix: kilo-
* SI Reciprocal Prefix: milli-
Quattuorvigintillion

The **quattuorvigintillion** is equal to 1075 (S), or 10144.

## Aliases

* Russ Rowlett - **Penteicosillion**
* Username5243 - **Tetreicosillion**

## Examples

* 1 quattuorvigintillion gallons of water would be a bit over the size of 3 galactic superclusters.
* SI Prefix: ictera- (S)/teczeta- (L)
* SI Reciprocal Prefix: tetreicoso- (S)/heptetetraconto- (L)
The Unity of Broadheart

The Unity of Broadheart is a large organisation created in 1963 that was founded in order to unite as many of the people in the downfall as possible and minimise conflict within the sunken quarter. Though it could be said that the broadheart's original plan had failed as the downfall is full of internal conflicts it is important to remember what the downfall would be like without the bit of peace that the broadheart creates. The broadheart has in general influenced the northern and cenrtral areas of the downfall the most with it's capital city, Pith being located in the heart of the dry jungle
Sexagintillion

A **sexagintillion** is equal to 10183 (S), or 10360 (L).

## Aliases

* Russ Rowlett - **Mehexacontillion**
* Username5243 - **Hexentillion**

## Examples

* The number of Planck volumes in the observable universe is ~300 sexagintillion.
* SI Prefix: exaka- (S)/hotnedaka- (L)
* SI Reciprocal Prefix: hexaconto- (S)/ennedekahecto- (L)
Mahlo cardinals

**Mahlo cardinals** are a type of large cardinal κ such that κ is both inaccessible and the set of weak or strong inaccessibles beneath them is *stationary* within them. An ordered set α is said to be stationary in κ if α intersects all the closed unbounded subsets β of κ (sets cofinal to κ and for which all the limit points of sequences of cardinality less than κ are contained in β).

## Discovery

Weakly inaccessible cardinals were formulated in 1908 by Felix Hausdorff under the name inaccessibles (*unerreichbare* or 'unreachable' cardinals). At this time they were just called "inaccessibles," and so too weakly Mahlos (weakly inaccessible κ such that the set of weakly inaccessibles beneath them are stationary in κ) were just called "Mahlo". They were discovered in 1911 by Paul Mahlo. In modern times the nomenclature is the other way around and "inaccessible" actually refers to the strong inaccessibles (discovered in 1930 by Sierpinski, Tarski, and Zermelo) while "Mahlo" refers to the strongly Mahlo cardinals (strongly inaccessible κ such that the set of strongly inaccessibles beneath them are stationary in κ).

## Definition

An equivalent definition of Mahlo cardinals to the one given at the outset is a set κ such that for all normal ordinal functions φ and elements α of κ there exists a regular fixed point of α ↦ φ(α) also within κ. Stating "all normal ordinal functions have a regular fixed point" (termed Axiom F) does not imply the existence of a Mahlo set but only says the universe is Mahlo (i.e. VM ⊨ ZFC + 「Axiom F」).

The reason that implication of the existence of regular fixed points for all normal functions is related to Mahlos is because the inaccessibles can be built up using iterated regular fixed points (i.e. imagine a Veblen-type hierarchy φ(αβ,...,α2,α1) where φ(α) is the (1 + α)th fixed point of β ↦ ρ(β) where ρ enumerates regular cardinals). Axiom F diagonalizes over this by quantifying over functions (a second-order logic operation) and thereby inaccessibility as a whole. The 1st Mahlo cardinal is therefore a limit of 0-inaccessibles (φ(α)), 1-inaccessibles (φ(1,α)), ω-inaccessibles (φ(ω,α)), hyper-inaccessibles (φ(1,0,α)), hyper-hyper-inaccessibles (φ(1,1,α)), super-hyper-inaccessibles (φ(2,0,α)), and so forth.

## n-Mahlo and hyper-Mahlo cardinals

In general, a cardinal κ is (α + 1)-Mahlo if the set of α-Mahlo cardinals less than κ is stationary in κ. For a limit ordinal α, κ is α-Mahlo if κ is β-Mahlo for all β < α. Naturally this can be extended in the same way inaccessible hierarchies can, so that hyper-Mahlos are defined as κ which are κ-Mahlo, hyper-hyper-Mahlos as κ which are κ-hyper-Mahlo, and so forth.

Because Mahlos are defined using generalization over regular fixed points they are useful in OCFs where they can be collapsed into inaccessibles and hyper-inaccessibles, which are like the bridge to Mahlos. In general large cardinal axioms do not have bridges between them as conducive to OCF analysis as this (i.e. the collapse of 0# implying cardinals or rank-into-rank cardinals is likely unknown).
-illion

The **-illion** is a notation and naming system used to systematically generate number names after million in English, and has variants in many other languages. The system makes an n-illion to equal to 103n+3 in the short scale, and 106n in the long scale, where n is the Latin prefix for the number. The short scale is mainly used in English-speaking countries, while the long scale in most of Europe. Non-Germanic countries have their own variation, such as the Indian counting system or the Japanese counting system. Sometimes they even deviate from a decimal system at all (e.g. the Ndom counting system).

## Extensions

* Largest Sequential Canon -illion - Vigintillion
* Largest Canon -illion - Centillion
* Largest Bowers Fanon Illion - Multillion

There are also many people on the internet who have extended -illions even further, such as febrillion and gothillion.
Boarding crew

(WIP) A group of people that board airmarines via various methods and use threats, hostages, weapons, explosives or other things to obtain goods. From important documents to heaps of rotsteel dust you will never find cargo that no boarding crew wants to steal and sell. Boarding crews often buy slaves from boarding schools to fill up spots of missing crew.

page not complete yet!
Googolxelp series

The **googolxelp series** is a series of numbers devised by Edwin Shade on 23 October 2021. It is a logarithmically based analogue of the googolplex, googolduplex, googoltriplex,. . ., series, only instead of raising a number to the power of 10 one takes the base-10 log of a number, beginning with the googol. In general, an N-xelp denotes the base-10 log of N, as xelp is plex spelled backwards.

## Series

The googolxelp series is divided into the real and complex xelpi (plural xelps is xelpi), where the complex xelpi are derived using the relation eπi = -1.

Real Xelpi
 Googolquadrixelp | log(log(2)) | -0.521390227

Complex Xelpi
Astrodelphis Starwing Saddle (Genesis: Part 2)

Astrodelphis Starwing Saddle

 DLC

Genesis: Part 2

Armor

 Type

Saddle

 Armor rating

30

Item

 Weight

20

 Stack size

1

 Added in

v329.5

**คำสั่งเสก**cheat gfi SpaceDolphinSaddle 1 0 0
**หรือ**
cheat giveitem "Blueprint'/Game/Genesis2/Dinos/SpaceDolphin/PrimalItemArmor\_SpaceDolphinSaddle\_Tek.PrimalItemArmor\_SpaceDolphinSaddle\_Tek'" 1 0 0

Crafting

 Required level

Level 120

 Engram points

60 EP

 Crafting XP

344 XP

 Crafting time

10s

 Crafted in

* Tek Replicator

 Required stations

 Refining Forge

Ingredients

**140 ×  Black Pearl**
**370 ×  Crystal or Primal Crystal**
**55 ×  Element**
**2500 ×  Metal Ingot or Scrap Metal Ingot**
**500 ×  Polymer, Organic Polymer, or Corrupted Nodule**

**Astrodelphis Starwing Saddle** เป็นอานสิ่งมีชีวิต ใน Genesis: Part 2. ใช้สำหรับการขี่  Astrodelphis. มันมาพร้อมกับไอพ่นทำให้ Astrodelphis สามารถใช้โหมดบินได้ที่แตกต่างกัน รวมถึงปืนใหญ่เลเซอร์ที่ยิงไปแล้ว โดนเป้าหมายทันที.

ฟังก์ชันในการควบคุมเกือบจะเหมือนกับ  อานของ Tropeognathus, เว้นเพียงแต่ใช้  Element เป็นพลังงานแทนการใช้  Gasoline, และ  Grenade เป็นกระสุนระเบิด.

แม้ว่าคำอธิบายจะระบุว่าสามารถใช้ได้เมื่อเรียนรู้เอ็นแกรมแล้ว, แต่ก็สามารถใช้ได้ทันทีโดยที่ยังไม่ต้องเรียน.

## โน้ต

* เป็นอานที่สองที่รองรับการขับเคลื่อนด้วยไอพ่น, อานแรกคือ  Tropeognathus Saddle.
* ปัจจุบันเป็นเพียง เอ็นแกรม/เทคแกรม ที่ต้องการเลเวลสูงสุดของผู้รอดชีวิตเพื่อเรียนรู้.
* การกดปุ่ม "ยิง" ค้างไว้จะเป็นการชาร์จกระสุนพลาสมาที่สามารถสร้างความเสียหายได้มากมาย.
* แพตช์การอัปเดต "เวอร์ 329.51" ลดขีดจำกัดสูงสุดที่สามารถสร้างได้จาก 684.3 เป็น 75.2 สิ่งนี้ทำให้อานที่มีเกรดสูงกว่ามีเกราะต่ำกว่า.
* อานสามารถพบเจอได้ใน Supply Crate บน Genesis: Part 2 เป็นวิธีเดียวที่จะได้รับมัน. นอกจากนี้ยังเป็นอานเทคเพียงชิ้นเดียวที่จะได้มาจากการลูท.
Axiom of Powerset

The **Axiom of Powerset** is an axiom in set theory which states that for every set A, there exists a set B containing all the subsets of A. In formal terms this is written out as `∀A∃B∀C∀D((D∈C ⇒ D∈A) ⇒ C∈B)`. Note that this exact sentence simply means every set A has a B containing *at least* all the subsets of A. It may contain more and so the Axiom of Specification would be needed to narrow this down to *only* the subsets unless the axiom were rephrased as `∀A∃B∀C∀D((D∈C ⇒ D∈A) ⇔ C∈B)`.

## Uses

* Powersetting allows one to keep on creating larger infinities given one infinity, as the powerset of any set is larger than that set. ZFC without powersetting would be limited to sets of size ℶ0.
* Powersetting is the means by which successive stages are built in the Von Neumann universe.

**Set theory**

**Theories**
Pocket set theory ★ Morse-Kelley set theory ★ Neumann-Gödel-Bernays set theory ★ Tarski-Grothendieck set theory ★ Zermelo-fraenkel set theory

**Axioms**
Axiom of Choice ★ Axiom of Extensionality ★ Axiom of Infinity ★ Axiom of Pairing ★ **Axiom of Powerset** ★ Axiom of Regularity ★ Axiom of Replacement ★ Axiom of Specification ★ Axiom of Union

**Objects**
Zero sharp ★ Von Neumann hierarchy

**Pioneers**
Abraham Fraenkel ★ Ernst Zermelo ★ George Cantor ★ John von Neumann ★ Kurt Gödel
Septyllion

The **septyllion** is equal to 10512 in the myriad system, or 10 squared 9 times.

## Full decimal expansion

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## See also

* Septillion
* Septilliard
Googolty

The **googolty** is equal to 10101, or 10100\*10. It is called **hundred duotrigintillion** (S), or **hundred sexdecilliard**.

## Full decimal expansion

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## Aliases

* Sbiis Saibian - **Googolbunch**
* Aarex Tiaokhiao - **Unpunoohol**, **101-noogol**
* Username5243 - **Googolnilex** = 10[0]10[1]100

## See also

* Googolteen
* Eleventy
* Twelfty
Null set

The **null set** is the set in set theory containing nothing. It is often written as {} or ∅.

## Properties

* Because of vacuous truth, the null set models every axiom in ZFC except for the Axiom of Infinity.
* Also on account of vacuous truth, the null set is a Grothendieck universe, which means it is transitive and closed under powersetting, repacement, and pairing.
* It is the intersection of every set and a certain element of that set, which will share no elements with that set.

**Set theory**

**Theories**
Pocket set theory ★ Morse-Kelley set theory ★ Neumann-Gödel-Bernays set theory ★ Tarski-Grothendieck set theory ★ Zermelo-fraenkel set theory

**Axioms**
Axiom of Choice ★ Axiom of Extensionality ★ Axiom of Infinity ★ Axiom of Pairing ★ Axiom of Powerset ★ Axiom of Regularity ★ Axiom of Replacement ★ Axiom of Specification ★ Axiom of Union

**Objects**
Zero sharp ★ Von Neumann hierarchy

**Pioneers**
Abraham Fraenkel ★ Ernst Zermelo ★ George Cantor ★ John von Neumann ★ Kurt Gödel
Ecosystem

(WIP) Various plants animals and fungi can be found in the downfall so they will all be listed here!

## Animals

* Aksel
* Roof Hound
* Hover Drake
* Vulture Bee
* Whirlwind Dragonfly
* Lapihorn Buck/Doe
* Quadridon
* Gale Crown
* Land Crab
* Ironcloud

## Plants

* Windweb
* Sweetkeg Bamboo
* Hammer Maize
* Mudwart
* Hull Moss
* The Bleeding Moon of the Great Airwell

## Fungi

* Cherry grass
* Salt cap
* Timberloaf
* Log yeast
* Land cloud
* Scilophagius dentritus
* Foothill miasma
* Wingorge
* Boastu
Aocillion

The **aocillion** (pronounced "/aho=sill=yun/") is equal to 10500. Despite ending with -illion, it is not a power of 1000.

## Decimal

100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## Aliases

* Jonathan Bowers - **Gogod**
* Sbiis Saibian - **Googolding**, **gogolchime**
* Username5243 - **Gooqnicol** = 10[1]500
Myriad

The **myriad** is equal to 104 = 10,000. It was first used by the Ancient Greeks and it also has its own name in eastern Asian naming systems, although in English the name is "**ten thousand**". In googology, it is used in Donald Knuth's -yllion system and the rare -yriad system.

## Properties

* Roman Numeral: **P** (formerly X with a bar)
* Ancient Egyptian Glyph: Bent Finger
Octyllion

The **octyllion** is equal to 101024 in the myriad system, or 10 squared 10 times.

## Full decimal expansion

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## See also

* Octillion
* Octilliard
Quindecillion

A **quindecillion** is equal to 1048 (S), or 1090 (L).

## Aliases

* Russ Rowlett - **Hexadekillion**
* Username5243 - **Pentadekillion**
* ??? - **Duodecyriad**

## Examples

* The Earth is composed of about 89 quindecillion molecules.
* A quindecillion atoms in a cube would be 1340 km wide.
* SI Prefix: pedaka- (S)/icxena- (L)
* SI Reciprocal Prefix: penteco- (S)/enneicoso- (L)
Quadridon

Large species of parrot that has a strange second pair of wings that are technically the same limbs as it's back legs. These Parrots are very intelligent and are one of the characteristic symbols of the Downfall. They can mostly be found in the dry jungle however they do appear around parts of the great cliff too.
Von Neumann hierarchy

The **Von Neumann** hierarchy is a way of building up the universe of sets in stages. Each stage is written in the form Va where a is an ordinal, beginning with V0 = {}. Every stage indexed by a successor ordinal is the powerset of the stage before and every stage indexed by a limit ordinal is the union of all stages before. In other terms:

* Va = P(Va - 1) when a is a successor ordinal.
* Va =

⋃

# b
0

b
<
a

V
b

{\displaystyle \bigcup\_{b = 0}^{b < a} V\_b}

The culmination of all possible stages is simply written as V and is the the universe of all sets. In set theories that admit classes this is definable but in set theories which do not one is limited by Vk in practice, where k is some ordinal number. If a stage Va can be treated like the universe of sets for a particular set of statements T0, T1, T2,. . . where all these statements are true, then we say that "Va models T0,T1,T2,. . .," denoted Va ⊨ T0,T1,T2,. . .

* Vω ⊨ All ZFC statements provided the Axiom of Infinity is excluded from the theory.
* Vω2 ⊨ All Zermelo set theory statements, a theory without the Axiom of Replacement.
* VI ⊨ All ZFC statements.

V0

V1

V2

V3

**Set theory**

**Theories**
Pocket set theory ★ Morse-Kelley set theory ★ Neumann-Gödel-Bernays set theory ★ Tarski-Grothendieck set theory ★ Zermelo-fraenkel set theory

**Axioms**
Axiom of Choice ★ Axiom of Extensionality ★ Axiom of Infinity ★ Axiom of Pairing ★ Axiom of Powerset ★ Axiom of Regularity ★ Axiom of Replacement ★ Axiom of Specification ★ Axiom of Union

**Objects**
Zero sharp ★ **Von Neumann hierarchy**

**Pioneers**
Abraham Fraenkel ★ Ernst Zermelo ★ George Cantor ★ John von Neumann ★ Kurt Gödel
500

**500 (five hundred)** is equal to 1/2 of a thousand. It's also called as **ream**, **short mease**, or **long ream**.

## Visualization

* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................
* ....................................................................................................

### In googology

* Latin Prefix: **quingenti-**
* Greek Prefix: **pentahecto-**
Septenvigintillion

The **septenvigintillion** is equal to 1084 (S), or 10162 (L).

## Aliases

* Russ Rowlett - **Octeicosillion** (not to be confused with octeicosillion)
* Username5243 - **Hepteicosillion** (not to be confused with hepteicosillion)
* ??? - **Unvigintyriad**

## Examples

* 1 septenvigintillion gallons of water would be about 16.5% the size of the observable universe.
* SI Prefix: iczeta- (S)/pectra- (L)
* SI Reciprocal Prefix: hepteicoso- (S)/trepentaconto- (L)
Stegosaurus factorial

The **stegosaurus factorial** was a factorial created by Edwin Shade on the Googology For Everyone Wiki sometime in mid to late 2020. It is denoted △(n) and is equal to 1!\*2!\*3!\*. . .\*n!, or

∏

# a
n

n
!

{\displaystyle \prod\_{a = 1}^{a = n} n!}

. The factorial derives its name from the fact that if one were to graph every number as a bar with a height corresponding to that number, the series of multiplications would resemble the tail or back plates of a stegosaurus.

## Lower Bound

The lower bound of n! is

n
n

e

n
−
1

{\displaystyle \frac{n^n}{e^{n - 1}}}

. Using this we can derive a lower bound for △(n) like so:

## Extension

The stegosaurus factorial has extensions based on the following hierarchy of functions:

* Δ
1

(
n
# )
Δ
(
n
)

{\displaystyle \Delta\_1(n) = \Delta (n)}
* Δ
m

(
n
)

∏

# a
n

Δ

m
−
1

(
a
)

{\displaystyle \Delta\_m(n) \prod\_{a = 1}^{a = n} \Delta\_{m - 1}(a)}

 when m is a successor ordinal.
* Δ
m

(
n
)

∏

# a
n

Δ

m
[
a
]

(
a
)

{\displaystyle \Delta\_m(n) \prod\_{a = 1}^{a = n} \Delta\_{m[a]}(a)}

 when m is a limit ordinal.

Fundamental sequences are most commonly defined as follows:

* ω

α
1

[
n
# ]

ω

α

⋅
n

{\displaystyle \omega^{\alpha + 1}[n] = \omega^{\alpha}\cdot n}
* ω

α

[
n
# ]

ω

α
[
n
]

{\displaystyle \omega^{\alpha}[n]=\omega^{\alpha[n]}}

 when

α

{\displaystyle \alpha}

 is a limit ordinal.

By the laws of ordinal arithmetic,

ω

0
1

[
n
# ]

ω
0

⋅
# n
1
⋅
# n
n

{\displaystyle \omega^{0 + 1}[n] = \omega^0\cdot n = 1\cdot n = n}

, which serves as the basis for all ordinals describable with just {0,

ω

{\displaystyle \omega}

} and addition, multiplication, and exponentiation in Cantor normal form. Past this, the stegosaurus factorial hierarchy (SFH) can be used in union with trigonotrassic ordinal notation (2TON).

## "Small" Values

### △(n)

* △(0) = 1
* △(1) = 1
* △(2) = 2
* △(3) = 12
* △(4) = 288
* △(5) = 34,560
* △(6) = 24,883,200
* △(7) = 125,411,328,000
* △(8) = 5,056,584,744,960,000
* △(9) = 1,834,933,472,251,084,800,000
* △(10) = 6,658,606,584,104,736,522,240,000,000

### △2(n)

* △2(0) = 1
* △2(1) = 1
* △2(2) = 2
* △2(3) = 24

1. ↑ Knuth, Donald. (Pub. 1997) "The Art of Computer Programming: Volume 1: Fundamental Algorithms 3rd Ed." *Addison-Wesley* https://proofwiki.org/wiki/Book:Donald\_E.\_Knuth/The\_Art\_of\_Computer\_Programming:\_Volume\_1:\_Fundamental\_Algorithms/Third\_Edition (Cf. https://proofwiki.org/wiki/Lower\_and\_Upper\_Bound\_of\_Factorial) Retrieved 19 October 2021.
Duotrigintillion

The **duotrigintillion** is equal to 1099, or 1/10 of a googol.

In L, it is known as **sexdecilliard**.

## Aliases

* Sbiis Saibian - **Googolchunk**
* Buddhist text - **Dvajagravati**

## Full decimal expansion

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## See also

* Untrigintillion
* **Duotrigintillion**
* Tretrigintillion
* Quattuortrigintillion
* Quintrigintillion
* Sextrigintillion
* Septentrigintillion
* Octotrigintillion
* Novemtrigintillion
Centillion

**Centillion** is the accepted name for the 100th -illion. It is equal to 10303 (S), or 10600 (L).

## Full decimal expansion

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Septillion

**Septillion** is equal to 1024 (S) or 1042 (L).

## Examples

* 1 liter of water contains about 33.4 septillion water molecules.
* The Earth weighs about 5.98 septillion kilograms.
* A sphere of a septillion gallons of water would be 19,000 km wide, 50% larger than the Earth.
* A tower of a septillion people would be 180 million lightyears high.
* A septillion dollars would cover the US with a layer of ~1 km thick.
* The observable universe is about 880 septillion meters wide.
* A septillion atoms in a cube would be 1.34 cm wide, about the width of a pinky finger.
* SI Prefix: yotta- (S)/tradaka- (L)
* SI Reciprocal Prefix: yocto- (S)/treco- (L)
Sextyllion

The **sextyllion** is equal to 10256 in the myriad system, or 10 squared 8 times.

## Full decimal expansion

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## See also

* Sextillion
* Sextilliard
Trigonotrassic ordinal notation

**Trigonotrassic Ordinal Notation** (TTON or 2TON) is an ordinal notation created by Edwin Shade which uses triangles to build up patterns that equal ordinals.

## Etymology

The name is from the Greek *trigonon* meaning triangle and the Middle English ‘truss’ meaning bundle, as in truss bridges, punned on with the word “Jurassic,” a reference to the time period the Stegosaurus lived in. This is fitting since this notation was made especially for the Stegosaurus Factorial, and the notation itself resembles both a stegosaurus’ back and bridge trusses.

## Definition

2TON is a “geometrically lexicographic” ordinal notation in that ordinals can be easily compared by seeing which structures come after other structures in the ordering. All structures are on a {3,6} tiling of cells which may either be empty or occupied. We order structures by measuring a portion of this tiling from a single triangle with its base parallel to the x-axis, called the *oritrigonon* (origin + trigonon). Every horizontal row of triangles is of descending priority from left to right, and the higher a row is from the oritrigonon the higher priority it has. (Higher priority means it’s closer to the front of the ‘alphabet’.) In this way we can order all structures contained within the “sextant” bounded by two extended lines of the oritrigonon in the {3,6} tiling. (A sextant is like a quadrant but one-sixth of the plane instead of one-fourth.)[See fig.1]

Triangles which have their vertex pointing up are called *upurntrigons* (up + turned + trigon) while triangles which have their vertex pointing down are called *durntrigons* (down + turned + trigons). Using this terminology, 2TON is defined like so:

* If no cells are filled except for the oritrigonon, the structure is equal to 1. [See fig. 2]
* If a structure is equal to the ordinal A, then the same structure with an upurntrigon filled in the next available empty cell in the oritrigonon row is equal to A + 1. [See fig. 2]
* The limit of a series of units which are all the same is one unit, then another unit but with a filled durntrigon placed in the first available slot in that unit, with every part of that unit after the filled durnitrigon removed. We tack on another upurntrigon at the end because a durntrigon can never precede an empty upurntigon. [See fig.3,4,5]

For practicality, we do not draw out the {3,6} grid every time but only the outlines of the filled cells, ignoring the empty cells.

The form of 2TON prior to ε0 is isomorphic to single-row BMS, where (n) is converted into a solid row of n + 1 upurntrigons and n durntrigons between the upurntrigons. From ε0 on new rules need to be introduced:

* For a series of lengthening expressions with units U1, U2,. . ., the limit is U1 followed by U2 with an upurntrigon placed in the highest priorty slot on top of that unit. Note an upurntrigon must always rest on a durntrigon unless it is in the bottom-most oritrigon row. [See fig.6]

The units must increment by a constant structure, otherwise they do not count as a valid series of units over which one can find the limit.

[To be continued. . . . . . .]
Googology Testing Wiki

**Welcome to the Googology Testing Wiki (GTW)!**
The GTW is a reincarnation of the former Googology Testing Wiki.

If anyone has time for googology, you can create articles. Don't copy pages, create something new, thanks.

## Staff

* Unnamed2019 (Founder, Bureaucrat, Admin)
* Vendellium (Bureaucrat, Admin)

*Need help building out this community?*

* Rules of this wiki
* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles

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

A **novemdecillion** is equal to 1060 (S), or 10114 (L).

## Aliases

* Jonathan Bowers - **Dugarguppy**
* Aarex Tiaokhiao - **Sooxagintol** (formerly **sxootol**), **60-noogol**
* Russ Rowlett - **Icosillion** (not to be confused with icosillion)
* Username5243 - **Enneadekillion**
* ??? - **Quindecyriad**

## Examples

* SI Prefix: nedaka- (S)/traczeta- (L)
* SI Reciprocal Prefix: enneco- (S)/heptetriaconto- (L)
Novemtrigintillion

**Novemtrigintillion** is the typical entry for the 39th zillion, equal to 10120 (S), or 10234 (L).

* SI Prefix: tracxena-

## Aliases

* Aarex Tiaokhiao - **Tetragintillion**, **longoogol**
* Username5243 - **Ennetrigintillion**
* Faketest (Cloudy176) - **Tetracontiad**
* Faketest (Username5243) - **Ennetriacontiad**
* ??? - **Trigintyriad**
Million

A **million** is equal to 1,000,000 = E6. It is both a square and a cube, thus it is a zenzicube or 6th power. It is often used as hyperbole or exaggeration to represent an indefinitely large number. The million is the last fully original English name, and 2 variants of a general illion system (short/long) are used to automatically generate power of 10 names after million.

## Properties

* A million seconds is about 11.5 days.
	+ Million Minutes: ~1 Year & 10 Months
	+ Million Hours: ~114 Years
	+ Million Days Ago (~2738 Years): Part of the Ancient Egyptian times.
	+ Million Weeks Ago (19,165 Years): Before the beginning of agriculture.
	+ Million Months Ago (~83,000 Years): Early Human Civilization + Sahara Desert - NOT a desert yet.
	+ Million Years Ago (Just 1,000,000 Years): Time of Homo Erectus (ancestor of modern humans)
* Sbiis Saibian computed that if a person walked 1000 miles per 31 days, after 75 years, that person would have managed to walk about 883,000 miles.
* On September 2007, Jeremy Harper had finished counting aloud to a million, and became known in the Guinness World Records.
* It would take 347 days for a faucet at full power to waste a million gallons of water.
* A million words is about 11 novels.
* A sphere of a million gallons of water is 11 times the height of an average person.
* A tower of a million people would reach 1700 km high, a bit higher than the ISS.
* Roman Numeral: M with a bar
* Ancient Egyptian Glyph: Man with Raised Arms