Introduction

If you're wondering how in the world Fictional Googology works, what it is, how to participate, whetever you're completely brand new, confused about some concepts, or just need to refresh your memory, you came to the right place!

This guidebook is meant to be (as the name suggests), the beginner's guide to this interesting and special community, containing the essentials and other necessities to this field.

And we'll even give you some tips on how to get started making your own numbers.

We hope that you leave this document with newfound knowledge and a headstart to your career in fictional googology!

~ The Fixing Fictional Googology Team

What is Fictional Googology?

Fictional Googology is the study of large, fictional numbers. It isn't meant as an actual rigorous field of study (although there are people who treat it like so).

Absolute Infinity (denoted as Ω or ת) here is an entry that is bigger than any finite or transfinite conceivable quantity. Every property of Absolute Infinity is also held by some smaller object, which fulfills the reflection principle.

But doesn't that mean all Fictional Googology entries falls under Absolute Infinity?

Yes, Fictional Googology may seem contradictory at first, because any property of any number in fictional googology should be held by Absolute Infinity. However, this is called Fictional Googology for a reason because it isn't real, and either are any of the numbers. Fictional Googology should be treated more like an artform then an actual field of study.

We'll cover some of the important concepts later such as:

• Classifications
• Notations
• Breakings
• Cycles (and its variants)
• Scales

...and so on and so forth. But first, we must understand the community's history to provide context for why things are done the way they are.

History of Fictional Googology

The history of Fictional Googology spans back multiple years, both on the rigorous and informal front. One of the first FGisms (Fictional Googologisms) is a number created by Mathis R.V on August 20th, 2021. It was on a video called "Numbers 0 to ABSOLUTELY EVERYTHING!!!".

Despite the lack of actual entries on the video, it was pretty clear what the final number was gonna be, judging by the title of the video.

This video inspired multitudes of “epistemological ascension”-type communities and has its effects in some internet groups. This video (or its concept) also was the foundation of one of the most significant parts of an FG video; Absolutely Everything Versions.

There is also general consensus that Fictional Googology began even earlier, back in June of 2021, Sergey Aytzhanov wrote a paper to go beyond Absolute Infinity mathematically, titled "The true magnitude of Absolute Totality".

This paper spawned off a major branch of numbers, called Hypergoogology, numbers that mathematically go beyond Absolute Infinity. It was also the basis for the majority of early numbers within the rigorous FG community.

What's next?

Let's explore the rest of history, starting at the NEVER series.

What is this branch?

Informal Fictional Googology (aka. Informal FG) is a sub-space of the wider Fictional Googology community that primarily resides on YouTube.

Like the name suggests, it is a more informal version of Fictional Googology, being meant and treated more like an artform then a real field of study. It also mostly doesn't have definitions or well-defined intrinsics, although there is an attempt of formalizing and standardizing many concepts being done by the BBN Foundation.

General Rules

There's some common communal rules/expectations that you should follow while participating in this field.

1: Numbers never end.

Fictional Googology is designed to be endless and infinite, so trying to end the entire number line by making an "End-All-Be-All" will absolutely cause problems and controversies.

This does not mean however you cannot end your own number line, as that is separate from the main path. Basically:

• You cannot end other's number line or the field entirely.
• You can end your own number paths and series.

Necessities

Before Cyclings

Before there was things such as Cycles and A.E. versions, we had simple numbers. Perhaps childish, and immature, but still some of the first entries within the community. Entries like Absolutely True End, or more ridiculously, Too Much Massive Finity (which by the way is a jumpscare).

Some of the earliest numbers were based around simple notations. Some were more complex, being full-span equations, but the early history started with just, simple functions. Things like the X notation for example.

Let's explore some of them shall we?

Notations

Early numbers within the community were based around extending on top of pre-existing notations that were defined before. We're gonna go through some of them.

The xX Series

First, we will start of with the xX Notation, as defined by Mathis R.V. The first thing we will need is a base function. Can be anything (eg. Ω₁).

It is called the X notation because it involves the letter X, which seems to be inspired by the multiplication function. Let's define how it works:

• A x B => B applications of some function A on top of A (eg. Ω x 4 => Ω_ΩΩΩ)
• A xx B => B rows of A x A x A ... (eg. Ω xx 4 => Ω x Ω x Ω x Ω)
  • A xxxx... B (with N x's )=> B rows of A xxx... (with N-1 x's) (eg. Ω xxxx Ω => Ω xxx Ω xxx Ω ...)
• A xX B => B x's within A xxx.... A (eg. Ω xX 4 => Ω xxxx Ω)

Seems simple so far right? Adding an extra "x" allows you to count rows of lower x's (eg. xxxx diagonalizes over xxx). xX then here diagonalizes over the "x" counts.

How do you diagonalize and count over rows of xX's? You add another "x", like so:

• A xXx B => B rows of A xX A xX ... (eg. Ω xXx 4 => Ω xX Ω xX Ω xX Ω)

You can see the pattern here right? If you keep adding another x to the operator you would eventually get to xXxX (which diagonalizes over xXxxx...).

Now we can keep this going and going but eventually we will need a way to express levels of "xXxX....", cause otherwise the text will overflow. This is where our next operator comes into play.

• (A xX A) x B => B counts of the letter "x" within A xXxX... A (eg. (Ω xX Ω) x 10 => Ω xXxXxXxXxX Ω)
• (A xX A) xx B => B rows of (A xX A) x (A xX A) x ... (eg. (Ω xX Ω) xx 3 => (Ω xX Ω) x (Ω xX Ω) x (Ω xX Ω) x Ω)

There's some implict behavior going on (like the auto-filling of the last "x Ω") but other then that, the notation seems, pretty simple right? You can again, have the same pattern for (A xX A) xX B and such, and then you get to the next level:

• ((A xX A) xX A) x B => B counts of the letter "x" within (A xX A) xXxXxX... A (eg. ((Ω xX Ω) xX Ω) x 4 => (Ω xX Ω) xXxX Ω)

Again, repeat the same patterns demonstrated before, and yes you can stack these, as highlighted below:

• ((Ω xX Ω) xX Ω) x 10 => (Ω xX Ω) xXxXxXxXxX Ω
• (((Ω xX Ω) xX Ω) xX Ω) x 10 => ((Ω xX Ω) xX Ω) xXxXxXxXxX Ω
• ((((Ω xX Ω) xX Ω) xX Ω) xX Ω) x 10 => (((Ω xX Ω) xX Ω) xX Ω) xXxXxXxXxX Ω

But we can't nest forever, that's where the next operator comes in.

• {A xX A} x B => B nestings of ((...(A xX A)...) xX A) (eg. {Ω xX Ω} x 4 => ((((Ω xX Ω) xX Ω) xX Ω) xX Ω) x Ω)

Can you do the same thing as before? Yes! You can apply "xX A)" to it also (eg. ({Ω xX Ω} xX Ω)) and it is still valid! You can even nest arrow brackets, and it'll expand out like expected:

• {{Ω xX Ω} xX Ω} x 2 => ({Ω xX Ω} xX Ω) x Ω
• {{Ω xX Ω} xX Ω} x 3 => (({Ω xX Ω} xX Ω) xX Ω) x Ω
• {{Ω xX Ω} xX Ω} x 4 => ((({Ω xX Ω} xX Ω) xX Ω) xX Ω) x Ω

Next "bracket pair" will be using square brackets (this time being described with patterns instead of definitions):

• [Ω xX Ω] x 2 => {{Ω xX Ω} xX Ω} x Ω
• [Ω xX Ω] x 3 => {{{Ω xX Ω} xX Ω} xX Ω} x Ω
• [Ω xX Ω] x 4 => {{{{Ω xX Ω} xX Ω} xX Ω} xX Ω} x Ω

And now the next bracket pair being /:

• /Ω xX Ω/ x 2 => [[Ω xX Ω] xX Ω] x Ω
• /Ω xX Ω/ x 3 => [[[Ω xX Ω] xX Ω] xX Ω] x Ω
• /Ω xX Ω/ x 4 => [[[[Ω xX Ω] xX Ω] xX Ω] xX Ω] x Ω

You should be able to see the pattern by now. The bracket pairs that are used for this sequence is (), {}, [], //, and ||. Afterwards, it stacks the previous brackets on itself, like so:

• (|Ω xX Ω|) x 2 => ||Ω xX Ω| xX Ω| x Ω
• (|Ω xX Ω|) x 3 => |||Ω xX Ω| xX Ω| xX Ω| x Ω
• (|Ω xX Ω|) x 4 => ||||Ω xX Ω| xX Ω| xX Ω| xX Ω| x Ω

Repeat the sequence, blah blah blah but now we need a way to represent infinite amount of brackets. This is where our next "bracket pair level" comes in.

• .|Ω xX Ω|. x 2 => { Ω xX Ω } x Ω
• .|Ω xX Ω|. x 3 => [ Ω xX Ω ] x Ω
• .|Ω xX Ω|. x 4 => / Ω xX Ω / x Ω
• .|Ω xX Ω|. x 5 => | Ω xX Ω | x Ω
• .|Ω xX Ω|. x 6 => (| Ω xX Ω |) x Ω
• ...

Sorry for the extra space, that's just markdown acting weird. If you know what the sequence is (reminder: (), {}, [], //, ||), then what this does is to basically count the nth bracket pair in the sequence.

Post-NEVER

Equation Complexities

Ordinal Levels

The Questionaire Regions

Cycles

Cycles

Stages and Classes

Breaking

Breaking is the act of exhausting a concept by continually counting higher and higher levels of the concept until you reach its limit.

There are several things you can break, such as classifications, cycles, hierarchies, and even things that wouldn't make sense like the act of breaking itself. Typically, after breaking the concept, a new higher form of the concept is used in order to continue use the idea.

There are many kinds of "breaking" values and levels. The pseudo-field of study for this is called Breakology, where you try to find how far you can exhaust something.

Entirallisms

Entirallism Levels is a small part of Breakology where some values require special conditions to count under such value.

Some of the values within this area are:

• Prebroken: When a value is broken before it was reached. Can be applied to all other levels.
• Visual: A value must be visibly seen to count under this.
• Actual: Based on technicality, it has to count.
• Literal: Values must be realistically possible within RL to count.
• Proper: Must be logically sound in order to count.
• Strict: There cannot be any other conditions for it to count.
• Empiricals: It must count under what the author thinks it is.

Loops

Sequences

Sequences are a concept created by SuperWindows78, which involves a cycling of a set of symbols or words that are used. These are similar to loops but rather then repeating previous numbers, it repeats your own set of symbols.

Like loops, each repeat makes the entry more powerful and increments the repeat counter.

These aren't often used within the community anymore, most sequences are from early-FG (???? [3] / LOE days), and we don't know why.

Mastery Sequences

Mastery Sequences are very similar to normal sequences, but instead of looping a set of symbols you loop the previous numbers. Also unlike loops, it also doesn't use a video for repeating the entries, you instead manually type in the entries and explictly state it is "mastered".

"Mastered" entries are basically overpowered versions of the respective, non-mastered variant. Some of the mastery sequences also has special effects that are applied on the number, however these has fallen out of fashion.

Decorated Functions

Delimiting Extendings

Higher Cyclings

Absolutely Everything Versions

Layers

Video Layers

Megaphoto Segments

Multiple Editors

Middle-Chaos Point

Scales

Powered Cycles

Quantum Googology

Quantum Googology is a sub-field of the Fictional Googology field which focuses on entries on the microsopic scale rather then the macrosopic scales. In other words, QG is about very small numbers, FG is about very big numbers.

Introduction

Now, let us take a different path. What if we approached Fictional Googology in a rigorous manner? Sure, the idea is still having fun making numbers, but now the fun is not primarily found in symbols or visuals, but rather the intricacies of the concepts and ideas operating behind the scenes... and in seeing how much the springs of logic can be stretched until they break...

What is this branch?

This is Rigorous FG (aka. rFG), a different and unique branch of the Fictional Googology community that is still just as much as an artform as the informal side. However, instead of writing up fancy functions and entries, you write up complex definitions with intricate details and arguments.

Basically, if FG was an actual field of study, this would be the closest thing to it.

Difficulties

Rigor Classifications

Collapses and u*-shifting

Primary Assumptions

What is "Everything"?

The SLs

Outside the "Outside"

RL Levels

Internality and Form

Transfiction

Supposability

Submetaness

Levels of Thought

First 2 TLs

End all, be all.

Uncollapsablity

TL3 and beyond...

The Second Sequence

Catareflection + Catamirroring

Abusing u*

Unsoundness

The Unitude Series

Metaness Layers

Conversational Mindgaming

Terms

• iFG => Informal Fictional Googology
• rFG => Rigorous Fictional Googology

The BBN Foundation

The BBN Foundation is an organization founded by Bored Thien and originally meant to house most of her projects. As of September 17th, 2025, the main goal of the BBN Foundation now is to standardize and formalize the concepts and designs used by the wider Fictional Googology community.