recursal/Fanatic-Fandom huggingface dataset:
Octovigintillion

An **octovigintillion** is equal to 1087 in the short scale. In the long scale, this number is known as a **quattuordecilliard**, whereas octovigintillion refers to 10168. An octovigintillion is also called **icosiennillion** in Russ Rowlett's Greek-based -illion system.

## Examples

* The compound SI prefix quettaquettaronna- multiplies by one octovigintillion.

## Decimal expansion

```
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[87]

## See also

**Tier 2**: millillion
Epstein system

The **Epstein system** of large number naming was devised by Louis Epstein starting in the late 1980s. It is a massive expansion of Chuquet nomenclature's long scale and a gateway into the somewhat greater Epstein Numbers.

The main page for it is at the lekno.ws web project "Counting really,Really,REALLY High" and there are articles at

* Big Numbers Wikia
* Massive Numbers Wiki

## Construction

The base prefixes of the Epstein system are described as follows:

* n-illion = 106n
* n-illiard = 106n+3
* n-illio-illion = 106\*106n
* n-illio-illiard = 106\*106n+3
* n-illia-illion = 106\*106n+3
* n-illia-illiard = 106\*106n+3+3

Where n is a semi-Latin prefix ranging from 1 to 1025-1. These can also be chained more, e.g. n-illio-illia-illiard = ((n-illio-illion)-illia-allion)-illiard. The prefix for n is constructed nearly identically to Bower's -illions except small SI prefixes are replaced with large ones, and Greek prefixes are used to multiply. For instance, a hecmegillio-illion = 106\*10600,000,000. & hecexillio-illion = 106\*10600,000,000,000,000,000,000.

Subsequent to the base prefixes,names are further extended through the use of apostrophes that denote the height of a power-tower
(e.g. *yottillia-illio'megillio-illion* for a million raised to a tower of a yottillia-illion megillions) and particle operators,as explained in the instructions for calculating the Immortal Storm Number.

Beyond the -illions named by the system are the Titled Numbers starting with the Immortal Storm Number,
then the Alphabet Numbers that build on the Titled Numbers,and then the **Epstein Numbers** and larger
derivatives thereof.

## List of numbers

* Deckilillion
* Megilliard
* Decmegillion
* Decmegilliard
* Hecmegillion
* Gigilliard
* Decgigillion
* Decaquadrillio-illion
* Quadrillia-illion
* Decillio-illion
* Vigintillio-illion
* Centillio-illion
* Kilillio-illion
* Megillio-illion
* Decmegillio-illion
* Hecmegillio-illion
* Decgigillio-illion
* Terillio-illion
* Exillio-illion
* Zettillio-illion
* Yottillio-illion
* Decaquadrillio-illio-illion
* Quadrillia-illio-illion
* Quintillio-illio-illion
* Centillio-illio-illion
* Kilillio-illio-illion
* Megillio-illio-illion
* Terillio-illio-illion
* Exillio-illio-illion
* Petillio-illio-illion
* Zettillio-illio-illion
* Yottillio-illio-illion
* Kilillio-illio-illio-illion
* Megillio-illio-illio-illion
* Exillio-illio-illio-illion
* Yottillio-illio-illio-illion
* Megillio-illio-illio-illio-illion
* Deca'quadrillio-illion
* Mega'megillio-illion
* Yottillio-illio-illio'yottillio-illion
* Megillio-illio-illio-illio'megillio-illion
Zillion Notation

**Zillion Notation** (ZN) is a BEAF-like notation created by CompactStar (formerly Nirvana Supermind) useful for coining zillions similar to the ones of Jonathan Bowers. It is similar in concept to the Extensible Illion System by the same user, although the latter is much older and ill-defined while the creator incisted the well-definedness and removed sourced and correct descriptions related to the ill-definedness (cf. The main article of Extensible Illion System and its sources 9, 10, ... ,18).

According to the creator, out of the many notations developed by the creator, it is the only well-defined one and the only one which has not been abandoned aside from Fast array notation.

## Definition

Let @ represent any sequence of non-negative integers separated by commas.

A valid expression in ZN is of the form z(@). ZN outputs a positive integer for every valid expression, determined using this set of rules:

* z() = 0
* z(a) = 1000\*a
* z(@, 0) = z(@)
* b > 0: z(a, b, @) = z(1000^a, (b-1), @)

If none of these rules apply, start the process shown below, starting from the second entry:

* If the entry is 0, then jump to the next entry.
* If the entry is not 0, then:
	+ Let n equal to this entry, and a equal to the first entry of the input.
	+ Decrease n by 1.
	+ Change the entry before n to a.
	+ Terminate the process.

## Examples

z(5, 2)

= z(1000^5, 1)

= z(10^15, 1)

= z(1000^(10^15), 0)

= z(10^(3\*10^15), 0)

= 10^(3\*10^15 + 3)

z(5, 0, 0, 1)

= z(5, 0, 5, 0)

= z(5, 0, 5)

= z(5, 5, 4)

= z(1000^5, 4, 4)

...

## Sources

1. ↑ CompactStar. Zillion Notation. Retrieved on May 16, 2022.
2. ↑ The first version of this article.
Quinvigintillion

One **Quinvigintillion** is equal to 10 to the power of 78, or 1078 in the short scale, While in the long scale, it is 10 to the power of 150, or One Novemquadragintillion in the short scale. 78 is also a triangular number, the twelfth one to be exact, meaning One Quinvigintillion is the twelfth number in the sequence of 10 to the power of x or 10x where x is a triangular number. One Quinvigintillion can definetly be put as 1063 (One Vigintillion) times 1015 (One Quadrillion), even though it is QUIN and not QUAD/QUATTOR.

## Examples

* The compound SI prefix quettaquettaexa- multiplies by one quinvigintillion.

## Decimal

```
1000000000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[78]

## See also

**Tier 2**: millillion
Quinquadragintillion

A **quinquadragintillion** is a cardinal number that represents an immense numerical value, specifically 10 to the power of 138 (10^138). In this context, the term "quinquadragintillion" serves as a convenient way to express and comprehend such a colossal number.

To put it into perspective, a quinquadragintillion is significantly larger than many familiar quantities. For example, the estimated number of atoms in the observable universe is estimated to be around 10^80 (one hundred **quinvigintillion**). Comparatively, a quinquadragintillion is astronomically larger, exceeding the number of atoms in the universe by an astounding factor of 10^58 (ten **octadecillion**).

## Examples

* "The estimated number of stars in the universe is often compared to a quinquadragintillion, demonstrating the immense scale of our cosmic surroundings."
* "In a mind-boggling feat of computation, the supercomputer was able to process a quinquadragintillion calculations per second, setting a new record in computational power."
* "The national debt of a country reached a staggering quinquadragintillion dollars, raising concerns about its long-term economic stability."
* "The probability of winning the lottery jackpot was estimated to be one in several quinquadragintillion, making it an incredibly rare occurrence."
* "During the brainstorming session, the team generated a quinquadragintillion ideas, exploring various possibilities and options for their project."

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 2^138
DTLOCF

Dropper Transfinite Leveling Ordinal Collapsing Function (DTLOCF) is a pseudo-ordinal notation that is based off of Dropper Transfinite Leveling (DTL) and Username5243 Ordinal Collapsing Function (UNOCF). It was created by Varyunya as an attempt to make a working, consistent, and low ambiguity ruleset for UNOCF. It shares a lot of properties with DTL and UNOCF, being based off of the ideas of "stage cardinals" from UNOCF and transfinite dropping and multi-entry subscripts from DTL. It is one of the first notations to utilize a fully working version of transfinite dropping, a concept that took the googology community years to figure out how to work without infinite-looping, giving it unprecedented strengths especially when compared to similar notations not using this concept. DTLOCF, along with DTL, once given a fully working ruleset, is projected to reach (0,0,0)(1,1,1)(2,2,2) in BM4. This makes it one the strongest of the dropper-based notations, even surpassing the likes of previous recordholders Strong Array Notation (SAN), R function, and Dropping Hydra made by legendary googologist Hypcos.

The definition for the most up-to-date version of DTLOCF is here (still a massive work in progress).

## Definition and Explanations (Still WIP)

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## References

1. ↑ https://docs.google.com/document/d/1o2Ps0MfaykOJQMVePxSHRX0xAxafEnBGHwjZqb7ohJk/edit

All images are from the work of Varyunya
Septillion

A **septillion** is equal to the cardinal number 1,000,000,000,000,000,000,000 or 1024. In the long scale, this number is known as a **quadrillion**, whereas septillion refers to 1042. The name is derived from the Latin prefix "octo-", meaning eight, and the -illion suffix (103x+3). A septillion does not have an official name in the modern-day Indian counting system. The only way it can be named is using compounds such as **one thousand crore crore crore** or **one lakh mahashankh**, although both terms are infrequently used in common parlance. A septillion is also called **oktillion** (not to be confused with octillion) in Russ Rowlett's Greek-based naming system.

## Examples

* The SI prefix yotta- multiplies by one septillion.
* The mass of Earth is approximately 5.972 septillion kilograms.
* There are around 1 septillion (10^24) stars in the universe, according to Space.com.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[24]

## See also

**Tier 2**: millillion
Asterisk Function

Asterisk function is a function that increases the scale of a number. It scales the number by doubling the digit by the same number so as n is now nn. Once the number has been doubled using the same digit, the number will be added to itself as nn+nn=nn. The formula for the equation is as follows: n>nn>nn+nn=nn.

Another asterisk function is called Double Asterisk function. In this function, n\*n, will be doubled on both sides like n and n both equal nn. Then both will be added to themselves in separate equations and the answers to these equations will be added together. The formula is as follows:

n1 n2 n1>nn1 n2>nn2 nn1+nn1=nn1a nn2+nn2=nn2b nn1a+nn2b=nn3

Numbers in the asterisk function increase exponentially:

0\*=0

1\*=1

2\*=22

3\*=4,444

4\*=88,888,888

5\*=4\*^2

This function is used to create very large numbers and a rapid pace. Though it is not as fast as other expansion functions, It is still a function that raises the number immensely. This function was used to create large numbers quickly, and represent very large numbers in a small representative notation. The asterisk function is very straightforward, and and even simpler to create larger numbers at a fast pace.
Quindecillion

A **quindecillion** is equal to 1048. In the long scale, this number is known as an **octillion**, whereas quindecillion refers to 1084. A quindecillion is also called **hexadekillion** in Russ Rowlett's Greek-based naming system.

## Examples

* The compound SI prefix exaquetta- multiplies by one quindecillion.

## Decimal

```
1000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[48]

## See also

**Tier 2**: millillion
Vigintillion

A **vigintillion** is equal to 1063. In the long scale, this number is known as a **decilliard**, whereas vigintillion refers to 10120. A vigintillion is also called **icosihenillion** in Russ Rowlett's Greek-based naming system. BlankEntity calls this number **Voogol**. It is the largest number name in most dictionaries excluding googol, centillion, and googolplex.

## Examples

* The compound SI prefix quettaquettakilo- multiplies by one vigintillion.
* The volume of the Virgo supercluster is approximately 3.54 vigintillion cubic kilometers.
* Physics theories suggest that sometime between 1034 (10 decillion) and 1064 (10 vigintillion) years from now, the protons found in the nuclei of all atoms will decay.

## Decimal

```
1000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[63]

## See also

**Tier 2**: millillion
Duodecillion

A **duodecillion** is equal to 1039. In the long scale, this number is known as a **sextilliard**, whereas duodecillion refers to 1072. A duodecillion is also called **trisdekillion** in Russ Rowlett's Greek-based naming system. Aarex Tiaokhiao calls this number **trecillion**.

## Examples

* The compound SI prefix gigaquetta- multiplies by one duodecillion.
* A duodecillion gallons of water in a sphere would be 1.9 quadrillion km wide.
* The great lakes contain roughly 52.92 duodecillion water molecules.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[39]

## See also

**Tier 2**: millillion
Quattuordecillion

A **quattuordecillion** is equal to 1045. In the long scale, this number is known as a **septilliard**, whereas quattuordecillion refers to 1084. A quattuordecillion is also called **pentadekillion** in Russ Rowlett's Greek-based naming system. Aarex Tiaokhiao calls this number **pentecillion**.

## Examples

* The compound SI prefix petaquetta- multiplies by one quattuordecillion.
* A quattordecillion gallons of water in a sphere would be 1.9 sextillion km wide.
* There are about 41.75 quattuordecillion water molecules in all the water on the earth.

## Decimal

```
1000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[45]

## See also

**Tier 2**: millillion
Googolplex

A **googolplex** is the number 10googol or 1010100. Writing a googolplex in physical form within the observable universe is impossible. A typical book can be printed with a million zeros. Therefore, it requires 1094 such books to print the decimal expansion of a googolplex. The name of this number is derived from googol. Googologists later took this number and made "-plex" to be a new suffix.

A googolplex has this name in Bower's illion system:

```
ten tretriotriaconto-tretrigintitrecentiduetriaconto-tretrigintitrecentimetriaconto-tretrigintitrecentitriaconto-tretrigintitrecentienneicoso-tretrigintitrecentiocteicoso-tretrigintitrecentihepteicoso-tretrigintitrecentihexeicoso-tretrigintitrecentipenteicoso-tretrigintitrecentitetreicoso-tretrigintitrecentitrioicoso-tretrigintitrecentidueicoso-tretrigintitrecentiicoso-tretrigintitrecentienneco-tretrigintitrecentiocteco-tretrigintitrecentihepteco-tretrigintitrecentihexeco-tretrigintitrecentipenteco-tretrigintitrecentitetreco-tretrigintitrecentitreco-tretrigintitrecentidueco-tretrigintitrecentimeco-tretrigintitrecentimeco-tretrigintitrecentiveco-tretrigintitrecentixono-tretrigintitrecentiyocto-tretrigintitrecentizepto-tretrigintitrecentiatto-tretrigintitrecentifemto-tretrigintitrecentipico-tretrigintitrecentinano-tretrigintitrecentimicro-tretrigintitrecentimilli-doetrigintitrecentillion

```

## Etymology

Milton Sirotta originally defined it as "one, followed by writing zeroes until you get tired". His uncle, Edward Kasner, unsatisfied by this vague definition, redefined it to its current value.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[9[100]]
Undecillion

An **undecillion** is equal to 1036. In the long scale, this number is known as a **sextillion**, whereas undecillion refers to 1066. An undecillion is also called **dodekillion** in Russ Rowlett's Greek-based naming system. Aarex Tiaokhiao calls this number **becillion**.

## Examples

* The compound SI prefix megaquetta- multiplies by one undecillion.
* An undecillion gallons of water in a sphere would be 1.9 trillion km wide.
* The electromagnetic interaction is around 1036 times stronger than gravity.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[36]

## See also

**Tier 2**: millillion
Novemdecillion

A **novemdecillion** is equal to 1060. In the long scale, this number is known as a **decillion**, whereas novemdecillion refers to 10114. A novemdecillion is also called **icosillion** in Russ Rowlett's Greek-based naming system. It is also called **gogolcrowd** using Sbiis Saibian's ExE name scheme.

## Examples

* The compound SI prefix quettaquetta- multiplies by one novemdecillion.

## Decimal

```
1000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[60]

## See also

**Tier 2**: millillion
One

**One** is the number equal to 1. It is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. Roman numeral is **I**.

1 is the multiplicative identity. It is the only number that is neither prime nor composite, so it is called a unit number (0 is the only other unit number). This means that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. For example, One is a Fibonacci number, regular number, odd number, factorial number, and a square number, cube number, etc. One is most commonly a determiner used with singular countable nouns, as in one day at a time. Almost all currencies have banknotes or coins with this number in the denomination.

All natural numbers are just strings of 1's added together. For example, 1,000,000 is a string of 1 million 1's added together.

## In googology

One has trivial properties in a surplus of googological functions. Here are some:

* One is a fixpoint of multiplication and all other hyperoperators in the left side, sharing this status with zero, meaning that 1[n]x=1 for n>2.
* One is the identity of multiplication and all other hyperoperators in the right side, meaning that x[n]1=x for n>2.

The Latin and SDN prefix for one is uni-, and the Greek prefix is mono-/haplo-.

1 appears frequently as a "default" argument in googological notations, such as BEAF, chained arrow notation, hyper-E notation, although some like phenol notation opt to use zero instead.

Because the reciprocals of large numbers are small, Sbiis Saibian argued that all numbers greater than 1 should be referred to as "large numbers." "Superuniary numbers" or "superuniaries," he called them. Because large and small numbers are "mirrored" around 1, it makes sense to refer to 1 as the largeness threshold. One could call a number like 1 + 1/googol a "very small large number." Of course, the smallest large number is a logical impossibility.

## As a cash denomination

Almost all currencies have this number as a cash denomination.
Nonillion

A **nonillion** is equal to 1030. In the long scale, this number is known as a **quintillion**, whereas nonillion refers to 1054. A nonillion is also called **dekillion** in Russ Rowlett's Greek-based naming system. Aarex Tiaokhiao calls this number **decillion** (not to be confused with the standard system decillion). He also gave name **thootol** and **30-noogol**, referring to the short scale value of this number. BlankEntity calls this number **phosphillion**.

## Examples

* The SI prefix quetta- multiplies by one nonillion.
* A nonillion gallons of water in a sphere would be 1.9 million km wide.
* A nonillion dollars would cover the world with a layer of 15,000 km thick.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[30]

## See also

**Tier 2**: millillion
Quattuorvigintillion

A **quattuorvigintillion** is equal to 1075. In the long scale, this number is known as a **duodecilliard**, whereas quattuorvigintillion refers to 10144. A quattuorvigintillion is also called **icosipentillion** in Russ Rowlett's Greek-based -illion system. Sbiis Saibian coined **lightweight** for this number.

## Examples

* The compound SI prefix quettaquettapeta- multiplies by one quattorvigintillion.

## Decimal expansion

```
1000000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[75]

## See also

**Tier 2**: millillion
Sexvigintillion

A **sexvigintillion** is equal to 1081. In the long scale, this number is known as a **tredecilliard**, whereas quattuorvigintillion refers to 10144. A sexvigintillion is also called **icosiheptillion** in Russ Rowlett's Greek-based -illion system. It can also be called **ogolbunch** in Sbiis Saibian's naming system since it is 10 times an ogol, although Sbiis Saibian has not actually coined that name.

## Examples

* The compound SI prefix quettaquettex- multiplies by one quattorvigintillion.

## Decimal expansion

```
1000000000000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[81]

## See also

**Tier 2**: millillion
Tredecillion

A **tredecillion** is equal to 1042. In the long scale, this number is known as a **septillion**, whereas tredecillion refers to 1078. A tredecillion is also called **tetradekillion** in Russ Rowlett's Greek-based naming system. Aarex Tiaokhiao calls this number **tetrecillion**.

## Examples

* The compound SI prefix teraquetta- multiplies by one tredecillion.
* A tredecillion gallons of water in a sphere would be 1.9 quintillion km wide.
* There is about 100 tredecillion grams of matter contained in the grand total of all the stars in the Milky Way Galaxy.

## Decimal

```
1000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[42]

## See also

**Tier 2**: millillion
Bently's number

**Bentley's Number** is equal to **Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest\_v1/":): {\displaystyle \sum^{9}\_{i=0}10\uparrow\uparrow i=1+10+10^{10}+10^{10^{10}}+10^{10^{10^{10}}}+...+10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}**
**Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest\_v1/":): {\displaystyle = 10,000,000,011+10^{10^{10}}+10^{10^{10^{10}}}+...+10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}**
, (here **Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest\_v1/":): {\displaystyle 10\uparrow\uparrow 0=1}**
) using Knuth's Arrow Notation. It is based on the story *Forever Endeavor*.

## Sources

1. ↑ [1]
2. ↑ A googol is a tiny dot
Graham's number

**Graham's number** or **Graham-Gardner Number** is a very large number, once claiming the title of the largest number used in a mathematical proof although this has since been surpassed by TREE(3). The number was coined by Ron Graham(1935-2020).

The number is the solution to how many dimensions a hypercube needs to make a configuration of colors unavoidable. In particular, it is connected to the following problem in Ramsey theory:

Join each pair of geometric vertices of an n-dimensional hypercube to create a complete graph of 2n vertices. This graph's edges should all be colored either red or blue. For what value of n does each such coloring have at least one complete subgraph that is only one color on each of its four coplanar vertices?

The number is equal to G(64) in the G function also defined by Ron Graham. The number is an upper approximation of the Graham-Rothschild number, which is also called the Little Graham.

## Computation

Graham's number can be computed easily using the G function:

G(1) = 3↑43

G(n) = G(n-1){G(n-1)}G(n-1)

Graham's number is equal to G(64). The 64 is quite arbitrary if the goal is to create as large of a number as possible, likely being chosen to approximate the Little Graham. If we input larger values, we can get the forcal, Graham Forcal, and some other numbers coined by Aarex.

This number can be approximated as 3{{1}}64 in expansion. The simpler Graham-Conway number is exactly 4{{1}}64.

The final digits of Graham's number are *not* easily computed by a simple application of algorithms for modular exponentiation.
Three

**3 (three)** is the positive integer following 2 and preceding 4. It is an odd prime number, the smallest number with both of those properties. Three is also the Fermat prime 220+1, along with the Mersenne prime 22-1, so it is the only Mersenne fermat prime. It is the smallest odd prime number and the only prime preceding a square number. It has religious or cultural significance in many societies. Its ordinal form is 3rd or third.

In base 10, it is easy to test for divisibility by 3 by simply summing the digits of the number. This is because 3 is a divisor of 9, the omega neighbor of 10.

3 is the number of non-collinear points needed to determine a plane, a circle, and a parabola.

## Properties

* Roman Numeral: **III**
* It is the fourth Fibonacci number.
* It is the first Mersenne prime, equal to 22 - 1.

## In googology

Three is often chosen as the basis for numbers computed using googological functions, due to many functions degenerating at 2. The SDN, Greek, and Latin prefix for 3 is **tria-**.

## Currency denominations

Some currencies, such as the Bahamian dollar and the Uzbekistani soʻm, have banknotes with this number in the denomination.

Some currencies, such as the Cuban peso and the Tajikistani somoni, have coins with this number in the denomination.
Sbiis Saibian

**Sbiis Saibian** (IPA: /sbiz saɪbjən/, born 1983) is an American recreational mathematician and "megalo-arithmologist" who is most famous in the googological community for maintaining a web book called *One to Infinity: A Guide to the Finite* (formerly *A Finite Journey*). In the book, he introduces and describes various googological notations and invents his own, called the Extensible-E System. The site was first publicly launched on December 9, 2008, four days after Googology Wiki was first created.

Saibian's output is prolific. As of March 2015, he has coined 15,610 googolisms (excluding beta releases), the second most for any single googologist, followed by Template:U. For comparison, this is over 44 times more than the number of googologisms (or as he calls them, "googolisms") coined by another famous googologist, Jonathan Bowers/Hedrondude.

"Sbiis Saibian" is a pseudonym, which he says was "invented by typing random letters on a keyboard." Another pseudonym he more recently goes by is Sbiis.ExE. His real name is not generally known.

 File:Bowman Intense VanishingPoint.png

## Notations invented by Sbiis Saibian

* Poly-cell notation (PcN)
	+ Stack notation (StN)
	+ Diamond notation (DiN)
	+ 5-cell notation (5cN)
	+ 6-cell notation (6cN)
	+ ...
* Extensible-E System (ExE)
	+ Hyper-E notation (E#)
	+ Extended Hyper-E notation (xE#)
	+ Cascading-E notation (E^)
		- Limited Extension Cascading-E notation (LECEN)
	+ Extended Cascading-E Notation (xE^)
	+ Hyper-Extended Cascading-E Notation (#xE^)
		- Hyper-Hyper-Extended Cascading-E Notation (##xE^)
		- Solidus-Extended Cascading-E Notation (/xE^)
* Saibian's Counter-Clockwise Arrow Notation: \(b \uparrow\uparrow\uparrow p = \_{p \leftarrow}b\), \(b \uparrow\uparrow\uparrow\uparrow p = b\_{\rightarrow p}\), etc.

## Specific numbers

* **203** is used as the base of the googologisms joe pellinger and grand joe pellinger by Sbiis Saibian.
	+ Its prime factorization is 7 × 29. It is also the 6th Template:W.
* **44,435,622** is used in the definition of the pseudomonarchia daemonum and the grand pseudomonarchia daemonum by Sbiis Saibian.
	+ It is equal to 6,6662 + 66. Its prime factorization is 2 × 3 × 7 × 11 × 96,181.

## See also

* Category:Numbers by Sbiis Saibian
* GWiki user page

## Sources

1. ↑ https://www.fictionpress.com/u/465777/Sbiis-Saibian
2. ↑ About Author - Large Numbers
3. ↑ Saibian, Sbiis. 3.2.3 - Ascending with Up Arrows. Retrieved on March 3, 2015.
4. ↑ Saibian, Sbiis. 4.3.10 - Extended Cascading-E Numbers Part IV (11871 - 14070). Retrieved on March 3, 2018.
5. ↑ Saibian, Sbiis. 4.3.11 - Extended Cascading-E Numbers Part V (14071 - 15610). Retrieved on March 3, 2018.

## External links

* Sbiis Saibian's Large Number Site
* Sbiis Saibian's General Site
* Beyond G and Large Number Lounge, S. Saibian's blogs
* Giga Gerard's review of Hyper-E Notation

Template:Googology fundamentalsja:Sbiis Saibian
zh:Sbiis Saibian
Billion

A **billion** is equal to the cardinal number 1,000,000,000 or 109 in the short scale. The name is derived from the Latin prefix "bi-", meaning two, and the -illion suffix (103x+3). In the long scale, this number is known as a **milliard**, whereas billion refers to 1012 (for which the prefix is tera-). In the Indian counting system, it is called a **hundred crore** or less commonly **arab**. Other names for this number are **gillion** (from giga-, in Rowlett's Greek-based system), and **naniad** and **gigund** which are fabricated terms appearing on various googological dumpsterbins. Like the million, it is often used as a hyperbole. Username5243 calls this number **goonvol**, and it's equal to 10[1]9 in UNAN.

## Examples

* Based on Jeremy Harper's 89-day-long count to a million, we can estimate that it would take more than 243 years to count to a billion, assuming sixteen hours are allocated for counting every day.
* The planet Uranus's surface area covers 8.1156 billion square km.
* The Big Bang occurred 13.8 billion years ago.
* The SI prefix giga- multiplies by one billion.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[9]

## See also

**Tier 2**: millillion
Sextillion

A **sextillion** is equal to the cardinal number 1,000,000,000,000,000,000,000 or 1021. In the long scale, this number is known as a **trilliard**, whereas sextillion refers to 1036. The name is derived from the Latin prefix "sexti-", meaning six, and the -illion suffix (103x+3). A sextillion is the first odd power of 10 that does not have an official name in the modern-day Indian counting system. The only way it can be named is using compounds such as **one crore crore crore** or **one hundred mahashankh**, although both terms are infrequently used in common parlance. A sextillion is also called **heptillion** (not to be confused with septillion) in Russ Rowlett's Greek-based naming system.

## Examples

* Based on Jeremy Harper's 89-day-long count to a million, we can estimate that it would take more than 243,000,000,000,000 years to count to a sextillion (about 17,600 times the age of the universe), assuming sixteen hours are allocated for counting every day.
* The SI prefix zetta- multiplies by one sextillion.
* The mass of the Moon is approximately 73.5 sextillion kilograms.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[21]

## See also

**Tier 2**: millillion
Duovigintillion

A **duovigintillion** is equal to 1069. In the long scale, this number is known as an **undecilliard**, whereas duovigintillion refers to 10132. A duovigintillion is also called **icositrillion** in Russ Rowlett's Greek-based naming system.

## Examples

* The compound SI prefix quettaquettagiga- multiplies by one unvigintillion.

## Decimal

```
1000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[69]

## See also

**Tier 2**: millillion
Quadrillion

A **quadrillion** is equal to the cardinal number 1,000,000,000,000,000 or 1015 in the short scale. In the long scale, this number is known as a **billiard**, whereas quadrillion refers to 1024. The name is derived from the Latin prefix "quadri-", meaning four, and the -illion suffix (103x+3). In the Indian counting system, it is called **ten crore crore** or a **padma**, although both terms are infrequently used in common parlance. The quadrillion is commonly-known but less so than a trillion, and some prefer to use **thousand trillion** or **miillion billion** instead. Other names for quadrillion include **small fry**, **guppycrumb** and **minnowspeck** which were systematically coined for use in Sbiis Saibian's Guppy Regiment, as well as **pentillion** in Russ Rowlett's Greek-based naming system.

## Examples

* Based on Jeremy Harper's 89-day-long count to a million, we can estimate that it would take more than 243,000,000 years to count to a quadrillion, assuming sixteen hours are allocated for counting every day.
* The US's national debt is approximately 31.305 trillion dollars as of Nov 2022.
* A cube with sides of 104 meters each would have a volume of a trillion cubic meters.
* The SI prefix tera- multiplies by one trillion.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[15]

## See also

**Tier 2**: millillion
Million

A **million** is equal to the cardinal number 1,000,000, 106, or E6. The word is derived from the early Italian *millione* (*milione* in modern Italian). It is both a square number and cube number. The million is sometimes used in the English language as a hyperbole or exaggeration to represent a very large number. In an Indian counting system, it is called **ten lakh** and is notated 10,00,000. Other names for million include **byriad** in the -yriad system, along with **niloogoltriplex** (the multiplicative equivalent of googoltriplex) by Username5243 and **sooixol** by HyperMess04. A million is the boundary between class 1 and class 2 numbers in Robert Munafo's idea. This number is equal to 10%6 in Hot notation.

## Examples

* Counting to a million took Jeremy Harper 89 days, during each of which he spent sixteen hours counting.
* The SI prefix mega- multiplies by one million.
* The country of India has a total area of 3287263 square kilometres (1269219 sq mi).

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[6]

## See also

**Tier 2**: millillion
Rayocircle

(SALAD)

The **Rayocircle** is equal to Circle(Rayo’s Number). The term was coined by Jiggyleaves930 using Steinhaus-Moser Notation. It is a lot larger than a Rayoplex or even a Rayoduplex.

This is computable only in Steinhaus terms (where a Steinhaus circle equals a Moser pentagon)...a Moser circle is undefinable as it is implied to have infinite sides.To compute it one would put Rayo's Number into Rayo's Number of squares,the innermost of which would resolve into Rayo's Number of triangles,each of which would resolve by raising its contents to itself,working outwards (the innermost being Rayo's NumberRayo's Number),until the final triangle from the first square would resolve to the value of the number of triangles in the second-innermost square,and so for each succeeding square until the outermost,whose outermost triangle would yield the final value.
Trevigintillion

A **trevigintillion** is equal to 1072. In the long scale, this number is known as a **duodecillion**, whereas trevigintillion refers to 10138. A trevigintillion is also called **icositetrillion** in Russ Rowlett's Greek-based naming system.

## Examples

* The compound SI prefix quettaquettatera- multiplies by one trevigintillion.

## Decimal

```
1000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[72]

## See also

**Tier 2**: millillion
Sinister Sight

"Strike fear into their hearts"

**Sinister Sight** is an unlockable passive item from the Mastema mod.

## Effects

* +0.5 Tears up.
* Gain homing tears.
* Tears have a chance to fear enemies.
	+ Scales with luck.
* Feared enemies take 1.5x damage from all sources.
* Turns your tears purple.

## Synergies

* Abyss: Turns Sinister Sight into a purple locust that has homing, a 15% chance to fear enemies, and deals 1x damage but deals 1.5x damage against enemies that are feared.

## Gallery

Item costume.
Xaro's Number

**Xaro's Number**(z'ah'r'oh's number) is approximately 10100100Ωε0∆~f\_φ(ω,0)(999)~f\_ψ(Ω\_ω)(100)Ω This number is physically and scientifically impossible to comprehend by the human brain as its so large. However we can still have a example using this number.

## Conclusion

Since **Xaro's Number** is approximately 10100100Ωε0∆~f\_φ(ω,0)(999)~f\_ψ(Ω\_ω)(100)Ω we can only get one example from it, However there is 56 myrillion. But we cannot add all of them or else that would take many many years.
Thousand

A **thousand** is equal to the cardinal number 1,000, 103, or E3. All -illion numbers are powers of a thousand in both the short scale and long scale (in the long scale, they are the powers of a million, or even powers of a thousand). In the short scale, a thousand is the 0th -illion. A thousand is commonly used for a separator for numbers in the decimal numeral system, with commas (or periods in some parts of the world) added at every power of a thousand. This number is colloquially known as a grand in English.

## Other names

Wikia user NumLynx gave the name triaplex for this number, coined in analogy to the trialogue.

Username5243 gave the names **niloogol** and **gootol**. The name niloogol refers to it being equal to 10[0]100 in Username5243's Array Notation, which is similar to googol's expression that is 10[1]100 but with 1 replaced with 0. The name gootol refers to it being equal to 10[1]3 in UNAN, which is 10[1]100 with 100 replaced with 3.

BlankEntity gave the name for this number **Koogol**.

DeepLineMadom gave the name **boogol**, and it is equal to 10[2]100 in DeepLineMadom's Array Notation. It is not to be confused with the much larger Bowers' boogol, which is {10,10,100} in BEAF, or \(10 \uparrow^{100} 10\) in arrow notation.

SeveralLegend9998 coined **goodol**, and it's equal to 10(1)100 in Hyperdimensional Array Notation.

## Etymology

It is probably ultimately a compound with indefinite meaning "great multitude, several hundred," literally "swollen-hundred," with first element from PIE root \*teue- "to swell," second element from PIE root \*dekm- "ten."

## Examples

* The SI prefix kilo- multiplies by one thousand. This has given rise to using K to abbreviate the number.
* In Greek prefix systems, the thousand is represented by kilo- (this is the origin of the SI prefix) and chillia-.
* The SI prefx milli- divides by one thousand.
* In Latin prefix systems, the thousand is represented by milli- (this is the origin of the SI prefix).
* Earth has a radius of 6,371 kilometers.
* Jupiter has a radius of 69,911 kilometers.
* You are required to have 1K subscribers to be monetized on Youtube.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[3]

## Sources

1. ↑ Part 1 - My Large Numbers
2. ↑ DeepLineMadom's googology - Numbers I've coined (Retrieved 4 May 2022)
3. ↑ SeveralLegend9998's Googology Series (Retrieved 25 October, 2022.)
Ackermann function

The **Ackermann function** is one of the simplest fast-growing binary functions. Ackermann function illustrates that not all total computable functions are primitive recursive. The Ackermann function is comparable to the lesser-known Sudan function and arrow notation, despite these two having slower growth rates. The prefix gag- is derived from this function with gag-n = A(n,n) (e.g. gagthree = 61).

## Definition

* A(0, y) = y + 1
* A(x, 0) = A(x - 1, 1)
* x > 0, y > 0: A(x, y) = A(x-1 ,A(x, y-1))
Satanic Ritual

**Satanic Rituals** are a special unlockable from the Mastema mod.

## Effects

* Standing in the center of the ritual causes the knife to rise up into the air then come down and stab the player, removing either 1 heart container or 2 soul hearts in exchange for a random permanent stat up between damage, tears, speed, and luck.
	+ There is a short cooldown between uses so that it doesn't continually remove health.
* The more times you play it, the stronger the stat increases will be.
	+ Can only be played up to 5 times.
* Only appears in Ritual rooms, one devil room layout, and one super secret room layout.
* Satanic Rituals cannot be bombed.

## Interactions

* The Lost/Tainted Lost: The ritual can only be used one time for either of these characters.
* Keeper/Tainted Keeper: The ritual will attempt to remove 15 coins before removing a heart container.
* Life Savings: Allows one free play without removing any health. The trinket will be removed instead.

## Gallery

Devil ritual room.Super secret ritual room.
Scientific notation

**Scientific notation** is a way of expressing numbers that are very large or small in the form s × 10e, where s is the significand or mantisa and . It may be referred to as **scientific form** or **standard index form**, or **standard form** in the United Kingdom.

Floating-point is a computer arithmetic system closely related to scientific notation, which expresses numebrs in the form (1 + s) × 2(e + b) where b is a bias that depends on the floating point format. This bias is added so that negative exponents can be represented, since the exponent is an unsigned integer.
Omega

File:Greek lc omega.png
**ω (omega)** is the smallest ordinal number.

In the Wainer hierarchy, the fundamental sequence of ω is (0,1,2,3,4...).

Aleph null is the cardinality of ω.

the symbol is the 24th letter of the lowercase **Greek Alphabet**.

## Hierarchies

fω(n) = {2,n,n+1}

Hω(n) = n+1

gω(n) = n

## Countable sets

If a set can be put into bijective correspondence with a subset of ω, it is countable. All finite sets fall into this category, and a set is *countably infinite* if it is both countable and infinite. Famous examples of countably infinite sets include the natural numbers, integers, rational numbers, and algebraic numbers.
Super Array Notation

**Super array notation** is a large numbers invented by Huge Numbers Wiki user RedBandServerYT.

This notation is ill-defined because the domain is not specified

## Rules

a<b> = a↑ba

a,n<b> = a↑bn

a,b<<1>> = {a,b,1,2}

a,b<<2>> = {a,b,2,2}

a<<b>> = {a,a,b,2}

a{b} = a<<<...<<<a>>>...>>> (b < and >'s with middle a) = {a,a,a,b}

a|b = a{{{...{{{a}}}..}}} (b { and }'s with middle a) = {a,b-1(1)2} = {a,a,a...a,a,a,b} (b-2 A's)

a∆b = {a,a(1)b}

aωb = {a,a(b)2}

a{ε0}b = {a,b((1)1)2}

a{ζ0} = X↑↑b & a

a{η0}b = X↑↑↑b & a
Quintillion

A **quintillion** is equal to the cardinal number 1,000,000,000,000,000,000 or 1018 in the short scale. In the long scale, this number is known as a **trillion**, whereas quintillion refers to 1030. The name is derived from the Latin prefix "quinti-", meaning five, and the -illion suffix (103x+3). In the Indian counting system, it is called **ten thousand crore crore** or **ten shankh**, although both terms are infrequently used in common parlance. The quintillion is commonly-known but less so than a trillion, and some prefer to use **million trillion** or **billion billion** instead.

## Examples

* Based on Jeremy Harper's 89-day-long count to a million, we can estimate that it would take more than 243,000,000,000 years to count to a quintillion (about 17 times the age of the universe), assuming sixteen hours are allocated for counting every day.
* The SI prefix exa- multiplies by one quintillion.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[12]

## See also

**Tier 2**: millillion
Septenvigintillion

A **septenvigintillion** is equal to 1084 in the short scale. This name is spelled **septenvigintillion** in Bowers' -illion system and **septemvigintillion** in Conway and Guy's -illion system. In the long scale, this number is known as a **quattuordecillion**, whereas septenvigintillion refers to 10162. A sexvigintillion is also called **icosioktillion** in Russ Rowlett's Greek-based -illion system. It can also be called **tiny twerpuloid-** in Sbiis Saibian's naming system, since it is a tiny twerpuloid divided by 10, although Sbiis Saibian has not actually coined that name.

## Examples

* The compound SI prefix quettaquettyotta- multiplies by one septenvigintillion.

## Decimal expansion

```
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000

```

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[84]

## See also

**Tier 2**: millillion
Luxembourg

**Luxembourg**, officially the **Grand Duchy of Luxembourg** is a landlocked country in Western Europe. It is bordered by Belgium to the west and north, Germany to the east, and France to the south.

Due to FIA Grand Prix naming regulations, the Nürburgring in Germany was raced as the Luxembourg Grand Prix twice in 1997 and 1998.
Crore

The **crore** is equal to 10,000,000 or 107. It is used in the Indian counting system and is a corruption of the Sanskrit word *koti*. A crore.is equal to ten million. It is written as 1,00,00,000' with the local 2,2,3 style of digit group separators. Countries' populations are frequently stated in crores; for instance, India's population in 2013 was roughly 125.2 crore.

## Examples

* Based on Jeremy Harper's 89-day-long count to a million, we can estimate that it would take more than 2.43 years to count to a crore, assuming sixteen hours are allocated for counting every day.
* There is no SI prefix for a crore, although **decamega-**/**decimicro-** (daM/du) are nonstandard compound prefixes for it.
* The Cenozoic period began 6.6 crore years ago.
* The star Rigel has a radius of 5.5 crore kilometers.

## Approximations

 Fast-growing hierarchy (Veblen hierarchy)
 Copy notation | 9[7]
Україна

**Україна** — держава, що розташована у Східній Європі, охоплює південний захід Східноєвропейської рівнини, частину Східних Карпат та Кримські гори. Межує з Румунією та Молдовою на південному заході, з Угорщиною, Словаччиною та Польщею на заході, з Білоруссю на півночі та з Росією на сході та північному сході. На півдні омивається Чорним та Азовським морями. Площа становить 603700 км 2 [5]. Найбільша за площею країна серед повністю розташованих у Європі. У світі Ізгальдини Україна відіграє дуже важливу роль. Хоча вона заснована на реальній країні, але оскільки дія у циклі книг Олега Євка відбувається у далекому майбутньому вона повністю відрізняється від справжньої України.

## Влада

У книгах Олега Євка Україною править президент Борислав Бондаренко.
Ballium's number

Ballium's number is a number coined in a parody YouTube video by Meerkats Anonymous, in which a fictional physicist Samuel Ballium claims it to be "the largest number."According to the video, Ballium's number is exactly
\[(794{,}843{,}294{,}078{,}147{,}843{,}293.7 + 1/30) \cdot e^{\pi^{e^\pi}}\]
In the video, a spoof on newscasts about scientific findings, Ballium explains how he accidentally added "Hamlet" to an equation he was working on and stumbled upon this number. The video also goes on to say that the "Microsoft calculator struggles to produce an output, even when set to scientific mode."
The number is in fact smaller than a googolplex. This can be shown easily enough, by rounding \(e\) and \(\pi\) up to the next nearest integer and replacing the first component with \(10^{21}\):
\[\text{Ballium's number} < 10^{21} \cdot 3^{4^{3^4}} = 10^{21} \cdot 3^{4^{81}} = 10^{21} \cdot 3^{2^{162}} = 10^{21} \cdot 3^{10^{162 \log\_{10} 2}} < 10^{21} \cdot 3^{10^{162 \cdot 0.4}} = \]
\[10^{21} \cdot 3^{10^{64.8}} < 10^{21} \cdot 10^{10^{64.8}} = 10^{21 + 10^{64.8}} < 10^{10^{64.8} + 10^{64.8}} < 10^{10^{65.8}} < 10^{10^{66}}\]
This is less than \(10^{10^{100}}\), so Ballium's number is smaller than googolplex.
In fact, \(10^{10^{66}}\) is a very generous upper bound. The actual value is closer to \(10^{10^{11}}\). It can be shown that:
\[10^{10^{11}} < \text{Ballium's number} < 10^{10^{12}}\]
Ballium's number contains roughly 138 billion digits before the decimal point, storage of which is possible on today's computers. However, the process of computing those digits exactly may be impractically long. The exact number of digits before the decimal point is 138,732,019,350.
Ballium's number is a typical example of common attempts to name a very large number. Its form seems to be largely inspired by Skewes' number, but it fails to be very large, mainly because the topmost exponent of the second component is too small.
Ballium's number is also an example of ultrafinitism.
Notes and references
↑ Largest Number Found - Youtube video
↑ Saibian, Sbiis. Ultimate Large Numbers List. Retrieved on May 20, 2013.