10,050 Pages

• ## Another proposal

I've noticed that when pages on numbers list all the different names people have given them, they phrase it in a way I don't like at all: "[person] calls this number [name]." It makes it sound like they're the names each of those people actually use to call those numbers in all their work, instead of just different names devised for the same number.

Other people may feel differently, but to speaking personally, things like all those extensions to Bowers' names for BEAF constructions that I devised years ago aren't anything I would say I "call" them, especially not in contrast to the names Bowers himself would devise later on in his updates to his large number pages. Hell, I don't even remember coming up with half of those names.

I suggest, i…

• ## Name the pattern?

March 23, 2018 by Meowzz

1. Take a Greek word

2. Take each letter of the word

3. Spell the letter

Eg. zero = μηδέν

• μ = μυ
• η=ήτα
• δ=δέλτα
• έ=έψιλον
• ν=nú

4. Take the letter spellings & repeat the process recursively n times.

BONUS

5. How many iterations until all letters of the alphabet appear?

• ## Reductio Absurdum

March 23, 2018 by Meowzz

In logic, ''reductio ad absurdum'' (Latin for "reduction to absurdity"; or ''argumentum ad absurdum'', "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.

Using down arrow notation, I purpose a fuzzification (the process of changing a real scalar value into a fuzzy value) function such that x | y would fuzzify y by x. In a recursive manner, in x | | | y, y would go thru the fuzzification cycle three times.

Motivations & other possible extensions / definitions to follow soon!

• ## The Code Phrase for the Day

March 22, 2018 by PsiCubed2

Higgs Boson Six

(if you don't know what this is about, it doesn't concern you)

• ## Rule Suggestion: Using image memes

March 22, 2018 by PsiCubed2

I propose that using image memes in the comment section be completely banned (including retroactively).

In my experience, these are nearly always used in an unrespectful and insulting manner. At least when used in coversation. You see these images alot in politics and religion debate boards, and their function is always derogatory. The whole point of using these things is to trigger the other person with a kind of visual "gatcha", which in my opinion has no place in a civil discussion.

So I'm putting this to the vote: Are you for or against such a rule?

Voting is open for registered users only, and only for those who registered before February 15, 2018.

It is perfectly fine to vote with a simple "Y…

• ## A request from everyone, regarding low quality content

March 22, 2018 by PsiCubed2

Recently we've got a flood of nonsensical and other low-quality blog posts and comments. I'm not talking about trolls (that's a seperate issue). I'm talking about regular users who sometimes flood the wiki with nonsense because they are bored or because they don't want to think things through.

So I respectfully ask everyone here:

Do not make any more low-quality comments, edits or blog posts. Humor is fine. Whimsical is fine. But there's a very clear line between having harmless fun and spamming discussions with garbage.

Thank you.

• ## A suggestion

March 22, 2018 by MachineGunSuper

So, this has probably been requested a few times before, but I'll say it too:

If you look in the recent activity, you will find about a hundred articles added to categories which don't have much of a use. First of all, that's just pure spam.

What I'm about to suggest will slow down trolls:

- a sort of system that doesn't allow any swear words to be written in the article

- a cooldown for how fast one can upload photos

-categories which don't serve much of a purpose should be instantly deleted. (not really instantly, but faster)

Say, a category like "numbers with 13249289285938593895839 digits to 1032932949295109 digits"

• ## My first official announcement as ADMIN of this wiki

March 22, 2018 by PsiCubed2

I've just waked up, and discovered I've been given ADMIN rights here. Not sure if my reaction should be "that's really cool!" or "may God have mercy on my soul", But I am sure of one thing: I've got a job to do and there's plenty to be done.

As my first action as a new Admin, I would like to assure everyone here that the current troll situation is being dealt with. Moreover: It will be dealt with in a smart manner.

I will not waste my time on cosmetic actions which have zero effect in the long run, which - unfortunately - means that in the short run it would seem as if I'm doing nothing. Rest assured that this is not the case.

Finally, an apology and two requests:

1, I deeply apologize for the way the administration left this place to die, until n…

• ## Psycubed

March 22, 2018 by Meowzz

Hi, I know you don't know me & I don't know you. I'm new here, so I don't really know anyone.

I went to school & was double majoring in math & philosophy. I dropp'd out my 1st year.

When I was 18, after graduating high school, but before starting college, I got into an infinite recursive loop in my head wondering what infinity raised to the infinith power would be. I talked w/ a friend of mine who was going to MIT & he asked me if I meant Taylor Series. At that point in time, my math level was AP calculus & I did NOT know about what he was talking about.

Fast forward to ~5 years ago when I start'd geting interest'd in Tree(3). Since then I have learned about tetration (infinite tetration would have blown my 18 year old mind), Ordinals, Card…

• ## TREE(3) vs SCG(2) which is bigger?

March 22, 2018 by Meowzz

It has been shown TREE(3) < SCG(3).

Is TREE(3) < SCG(2)?

Edit: Will be doing a bigger edit to this post soon to integrate new info!

https://en.wikipedia.org/wiki/Friedman%27s_SSCG_function

• ## Down arrow notation

March 22, 2018 by Boris Huller
• ## The Code Word, for whomever it concerns

March 21, 2018 by PsiCubed2

No longer relevant. New Code Phrase will be issued on request.

• ## ztan numbers: a newbie's attempt at making numbers that end up in exponential level

March 21, 2018 by Antimony Star

this is my first attempt at making a large number, and I tried to make it without recursion.

define

, which makes this function grow exponentially.

• ## Non-Arbortrary Treenomials

March 21, 2018 by Meowzz

Objectiveto perpetually find better and better ways to "name" larger and larger numbers.

Treenomial Notation aka Tree-Name Notation (#WIP)

Looking for any input on notation for my Forrest Functions.

Bird's Array Notation has been suggested in a previous post.

Thanks for feedback (:

• ## Smallest Number Study

March 21, 2018 by Meowzz

If Googology is for large numbers what is "the practice/craft of generating, comparing, and naming small numbers and the study and theory of how to do so"?

Note: You can multiply any number by 0 safely; the same cannot be said for 0 & division. Point being, things can be different when approached from different angles.

• ## Diagonilization

March 21, 2018 by Meowzz

If f0(0)=scg(tree(0)), using diagonilization, define the supremum

• ## The whole googology in one diagram

March 21, 2018 by Scorcher007

For languages of set theory (1st). For arithmetic languages (2nd)

• ## Proposal re: all those categories for numbers people are making

I know I said I would leave this wiki, but I'm here to propose a rule to stop something I deem highly disruptive and wasteful to this wiki.

A lot of people have been making categories for things like "2 times square", "5 times square", humble numbers, squarefree numbers, non-pandigital numbers, sphenic numbers, semiprimes, Fibonacci numbers, repdigits... it goes on.

I propose a rule where we ban giving numbers any categories based on numerical properties except for prime numbers, non-powers, and maybe perfect powers of a base no more than 10. It seems to me like a thing people just do when bored, rather than due to serious interest in maintaining a professional and well-organized wiki. The furthest I'm willing to go with these categories is giv…

• ## SATCLN III

March 20, 2018 by Lord Aspect

final part of it

i am going to BLOW THIS PIECE OF JUNK OUT OF THE STATUS OF LARGEST NUMBER.

symbol e

e = 3^^^3

e0 =e^^^....(e times)...^^^e

e1 = e0^^^.....(e0 times).... ^^^e0

e2 = .....

e10^^^100 = E

E^^^(E times)^^^E = E0

E1 = E0^^^(E times)^^^E

...

E(10^^^.....(E times).....^^^100) = d

things are getting really huge here

d0 = d^^^^^^.........(d^^^d times).......^^^^d

d1 = d^^^^.....(d0^^^d0 times)....^^^d0

...

d(d(10^^^100)^^^^...... (d(10^^^100)-1 times)....^^^d(10^^^100)) = D

D0 = D tetrated to D

D1 = D0 tetrated to D0

...

DD = D(D - 1) tetrated to D(D - 1)

....

DDDD......(D times).....DDD = c

c0 = c^^^(c^^^(c^^^(c^^^..........(c times in total)....^^^c)^^^c

c1 = c0^^^(c0^^^.......... i hope you got how it repeats

...

c(10^^^100) = C

C0 = C^^^.......... (C tetr…

• ## BIIGGG NUMBERES!!!

March 20, 2018 by Jolly Yellow Discus

biggss numbers is defined as Q_1=n^n, where n=123456789123456789123456789123456789123456789123456789123456789123456789123456789012345678912345678.

It big numbder!!!!

• ## Surreal Numbers

March 19, 2018 by Meowzz

Super interested in the construction method & modifying it by allowing equality in Axiom 1.

Any others interested in surreal numbers?

See

• https://en.wikipedia.org/wiki/Surreal_number
• ## Googology Bookclub Meeting I - (One to Infinity: A Guide to the Finite/1.1.1 Welcome to the Numberscape)

March 19, 2018 by DecskySikh34311

For this gathering of the Googology Bookclub the reading material was part one of chapter one of section one of Saibian's online web-book, One to Infinity: A Guide to the Finite. Firstly, before providing my thoughts on it I must apologize for not specifying that only this part of chapter one will be considered, rather than the entirety of chapter one, which may be a lot to read in one day.

Well, firstly let me say my favorite part was the last section, The Call to Adventure... at the end. It really gave me a feeling of excitement to know that I was embarking on a journey of knowledge that spanned across the months it must have taken to write this and polish it, and that here was a person who was willing to explain everything out as if I had neve…

• ## SATCLN II

March 19, 2018 by Lord Aspect

Silly Attempts To Create Large Number II

starting from a new huge number notation

Q0 = 2^3^4^5^6^7^8^9.................^(10^100)

Q1 = Q0^(Q0 + 1)^(Q0 + 2)^.......................(Q0 ^ Q0)

Q2 = ......

....

Q(Q2^Q3^Q4^Q5^Q6^..................^QQ1) = QX

QX0 = QX^(QX + 1)^(QX + 2)^...........^(QX tetrated to QX)

QX1 = QX0^(QX0 + 1)^............^(QX0 tetrated to QX0) ....... QX(QX) = QZ

QZ0 = QZ^(QZ + 1)^.....

QZ(QZ(QZ(QZ0))) = Aq

Aq = Supreme Aspectplex

• ## "Bigger" notation

March 19, 2018 by PolyhedralMatrix102

"Bigger" notation is defined according to the Sass(n) function, which I already did.

make a⇄b=a↥Sass(n)b, now make ⌇ equalto the proof theoretic ordinal of ZFC+any theorem that will be thought of.

the number I call "biggestillion" is equal to 708010⇄Sass(BIGFOOT)

this easily beats my earlier largest googolism by a landslide!

• ## Counting to Zero by 0

March 19, 2018 by Meowzz

A book (in progress) about how Zip & Zilch make Zero

Scene 0  (A Love Story?)

We find our heros zip & zilch in the middle nowhere w/ nothing to be found..

A Case Of Mistaken Identities

"It depends upon what the meaning of the word equals equals" -Bill Clinton?

Equality & Equivalence (From General Relativity to Absolute Specificness)

Itô's Dilemma

Stochastic Series (Random Walks in Random Fields & Fuzzy Forests)

Euler's Day Off

Triangles & Trees (Euler's Line, Tree Functions & Subcubic Graphs)

Waiting For Godel

Incompleteness & Halting (Turing Machines & Busy Beavers)

Cantor Won't?

Infinite Recursion (Ordinals & Cardinals)

The Poincaré Plot Thickens..

Recurrence relations (Difference Equations & Imaginary Irrationals)

Descartes Before the Horse

Order of Op…

• ## Arborocity

March 19, 2018 by Meowzz

Initial Thinking

Forest (hypertree) functions could be used to count trees.

Forest numbers would be equivilant to ordinality.

Then

I found a post from @hyp_cos TREE into SVG.

I then found this gem from @hyp_cos which states:

• When we go through all the forests, we get a limit of ε0.
• Using forests and self-loops, we get ε1.
• Using forests and no-fused cycles, we get ϑ(Ωω), or SVO.
• The set of forests made from them (you can use different cycle-one-edge-fusing-trees) reaches BHO.

This seems to confirm my initial thinking regarding the correlation of tree : forest.

Currently

Working on a jungle number extension such that jungle numbers (considering a jungle to be an inaccessible hyperforest) would map to cardinality.

Also working on the correlation of rose …

• ## Cloud(99)!(WiP)

March 18, 2018 by Meowzz

CLOUD(z)

• TREE(z)
• SCG(z)
• FISH(z)
• BIRD(z)
• BEAVER(z)
• WORM(z)
• OKOJO(z)
• SASQUATCH(z)
• GUPPY(z)

See

• http://googology.wikia.com/wiki/TREE_sequence
• http://googology.wikia.com/wiki/Subcubic_graph_number
• http://googology.wikia.com/wiki/Fish_numbers
• http://googology.wikia.com/wiki/Bird%27s_array_notationhttp://googology.wikia.com/wiki/Bird%27s_array_notation
• http://googology.wikia.com/wiki/Busy_beaver_function
• http://googology.wikia.com/wiki/Beklemishev%27s_worms
• http://googology.wikia.com/wiki/Okojo_numbers
• http://googology.wikia.com/wiki/Sasquatch
• http://googology.wikia.com/wiki/Guppytriplex
• ## Beklemishev's Worms python code

March 18, 2018 by QuasarBooster

• ## Bigger roman numerals

March 18, 2018 by Unknown95387

You probably already know it, but there are bigger roman numerals than just M = 1,000. You know that there are roman numerals that we know from school:

Roman numeral Number
I 1
V 5
X 10
L 50
C 100
D 500
M 1,000

... and that was all.

There are bigger roman numerals. It's not written badly, like MMMMMMMMMM = 10,000 and so on. The bar on the top of the numeral means "times 1,000". In this case, 1,000 is also equal to $$\bar{\text{I}}$$ . So it's :

Roman numeral Number
$$\bar{\text{V}}$$ 5,000
$$\bar{\text{X}}$$ 10,000
$$\bar{\text{L}}$$ 50,000
$$\bar{\text{C}}$$ 100,000
$$\bar{\text{D}}$$ 500,000
$$\bar{\text{M}}$$ 1,000,000

Combining numerals isn't hard.

4,000 = $$\text{M}\bar{\text{V}}$$ or $$\bar{\text{IV}}$$

6,000 = $$\bar{\text{V}}\text{M}$$ or $$\bar{\text{V… Read more > • ## Googology Bookclub Idea March 18, 2018 by DecskySikh34311 Hello community! Today there is idea I came up with, which is both educational and fun. Recently, I noticed that there's been a lot of salad numbers and not-so-original notations, (hey, no offense, just pointing something out!), and so I thought: "what better way to encourage stronger notations than to learn from the experts themselves?" So this is the zeroth meeting, (the zeroth rather than the first because no-one was given advanced warning of it), of what I proudly present as...(pause for dramatic effect)...the Googology Bookclub! Hold on, let's try that again... - of what I proudly present as...(pause for dramatic effect)...the There, fancy font makes anything better! For every meeting of this bookclub, I will share what I've personally learne… Read more > • ## I did another thing March 18, 2018 by Alemagno12 • ## woah! March 17, 2018 by PolyhedralMatrix102 look here and youll find a wiki just like this one with 868 pages, where more and more pages are being added as we speak. what is the point though if we already have googology wiki? these pages seem to be coming from this guy by the way. Read more > • ## googology expressions March 17, 2018 by PolyhedralMatrix102 "shoot for the stars so you land on the moon!" "where there's a will there's a way" "don't let your schooling interfere with your education" "don't make mountains out of molehills" "shoot for the large uncountable ordinals so you land on huge countable ones, which in turn will reduce down to massive finite numbers in some notation or hierarchy" wait a minute, this is like how ginger ale fizzes when put into the cup and there's a bunch of foam at first but then it like settles and goes down, only in the math world "where there is an unsticking symbol like \(\Omega$$ or $$I$$ there is a way"

"don't let the overly complicated math terms of wikipedia and other sites deter you from going farther than you know youre capable of"

"make continents out of a…

• ## Silly attempts to create really huge number

March 17, 2018 by Lord Aspect

I decided to create a number enormously larger than Aspectplex (and it's factorial (and aspectplex tetrated to itself)).

I don't know if i will succeed.

For first, i need notation, that allows to make larger numbers in shorter ammount of calculations and iterations.

Attempting to tetrate it to itself: 3^3^3

the result is 7625597484987

so 7625597484987 = σ1

σ2 = σ1 tetrated to itself

then, we are going to repeat this for some time.

will σ2000 be enough?

i think no

i need larger number

this notation makes larger and larger numbers with each iteration

to calculate larger numbers, we have to use another notation

where σσ3 = 2σ3, or σσσ3 = 3σ3

i hope you got it

so, our next number is going to be (σ2000)σ(σ2000)

still need larg…

• ## biggest notation ever thought of or WILL be thought of!

March 17, 2018 by PolyhedralMatrix102

sorry, the blog went up by accident

um, let's see, for a BIG notation...how about...this:!

Sasquatch has something to do with 12^^12. Now define Sass(n) function as like function to make Sasquatch, but it can have ANY value for n! Sassa(n) is like fa(n) in growing hierarcht, only with base rule of f0(n)=Sass(n)!

Define Sass(10000000), where ₰ is largest ordinal out of theory with SASQUATCH symbols, for honor of SASQUATCH inventor

This is new largest googogism.

March 16, 2018 by PolyhedralMatrix102

In Googology I've heard people speaking about "inaccessible" cardinals or ordinals - what are these precisely? I understand what the Church-Kleene ordinal is and what $$\Omega$$ is, but what is an "inaccessible" cardinal?

I ask this because I've heard people talking about it here, and it puzzled me.

• ## happy late pi day or something

March 15, 2018 by Alemagno12

no i still haven't dedicated enough time to fully memorize other digits

• ## Aspectplex

March 15, 2018 by Lord Aspect

For first, you have to undestand my notation

let's imagine number a1

a1 = 3! (1 * 2 * 3) (6)

a2 = a1!! (1 * 2 * 3 * 4 * ... * (a1! - 1) * a1!)

a3 = a2!!! (1 * 2 * 3 * 4 * ... * (a2!! - 1) * a2!!)

...

a200! = α (Aspectplex)

• ## Happy Pi Day!

March 14, 2018 by Daniellewiki

Happy Pi Day everyone! This is the 30th anniversary of Pi Day! I'm someone who really loves memorizing digits of the value of pi!

These are the digits I have memorized so far 3.1415926535897932384626433832795028841971693993751058209

• ## Proof that negative tetration is impossible

March 13, 2018 by ArtismScrub

At first, you'd think that:

a↑↑(-b) = 1/(a↑↑b)

analogous to exponentiation.

However, this does not work with how tetration is defined:

a↑↑(b+1) = a(a↑↑b)

Instead, this definition can be generalized backwards towards:

a↑↑(b-1) = loga(a↑↑b)

So, this means:

a↑↑1 = a by definition

a↑↑0 = loga(a) = 1 (this is true for all a)

a↑↑(-1) = loga(1) = 0 (this is true for all a)

a↑↑(-2) = loga(0) = nope (as loga(n) approaches 0, the result approaches negative infinity)

• ## I'm taking a very long break

March 13, 2018 by PsiCubed2

I came here to discuss googology, and not to deal with juvenile trolls.

And I'm not talking just about Edwin Shade here. He is just the last straw of a worrying trend that has been going on for months now. Please don't take it the wrong way, but this place has turned into a complete farce.

Normally in such a situation, my insticts are to stay and try to fix things. But I've come to the conclusion that I simply do not have the time to do this properly, and that doing a half-assed job is worse than doing nothing. Especially since I'm going to have my hands full IRL for the next year or so.

So I'm taking a very very long break from participating here. Don't know how long, but it is unlikely to be less than a year. This includes updating my blog p…

• ## Googolgogolthroogoltoogolroogolboogoldroogoldexplexplexplex Transfinity

March 13, 2018 by Shang Shang Yang

prepare for the true meaning of "big" as you see endless digit below

Googolgogolthroogoltoogolroogolboogoldroogoldexplexplexplex Transfinity is (BIGFOOT^BIGFOOT BIGFOOT times +1)*123456789123456781234567123456123451234123121

March 12, 2018 by Daniellewiki

Are there any pages that could use some pictures? I want to add some pictures to articles but I can't really find any articles to add pictures to.

• ## Teratetrisplextrexdexoblexplexplexdextroqex Googolaxeplexinfinopleafininfinite Infinity

March 11, 2018 by Shang Yang Yang

Will you like infinity? This is 1010101010101101010101010101010101001010010110010010101010101010101010101010001010101010101*11000010101010101010101010101001010101010101010101010*1010*Big Bin. Big Bin is BIG FOOT-110110110001

• ## Bijective storing ordinals in infinite computer memory

March 10, 2018 by Rgetar

Infinite computer memory is sequence of bits. They can be enumerated: bit 0, bit 1, bit 2 etc.

Ordinals up to ω are natural numbers. Natural numbers can be represented in binary form, that is as sequence of bits, which can be enumerated from the right. Natural number can be stored in computer memory as binary number, that is

bit 0 is bit 0 of the natural number

bit 1 is bit 1 of the natural number

bit 2 is bit 2 of the natural number

...

Ordinals up to ω2 can be represented as ωc1 + c0, where c0, c1 - natural numbers.

Way of storing ordinals up to ω2 in computer memory:

bit 0 is bit 0 of c0

bit 1 is bit 0 of c1

bit 2 is bit 1 of c0

bit 3 is bit 1 of c1

bit 4 is bit 2 of c0

bit 5 is bit 2 of c1

bit 6 is bit 3 of c0

bit 7 is bit 3 of c1

...

Ordinals up to ω3: ω2…

• ## Contribution Question

March 8, 2018 by BlauesWasser

I have a question. I have seen people making their own numbers/functions/notations and making a page for them.

Can I do that? Or have those people given specific permissions?

• ## March Googology Improvement Plan ~ Administrator Nominations and A Greeting Message

March 8, 2018 by 👽

Due to recent events, it has been ever more clear to me that we are in need of a new generation of admins. Granted, there are already enough admins to moderate content, it is simply that the only active admin is Cloudy176, and he often faces criticism for his comical take of events.

While is it true he is rather relaxed by the standards of other wikis, I think this is really just proof that it would be healthier if others were appointed admins, so that the surplus of one admin might counteract the deficit of another, (no, I'm not calling Cloudy's sense of humor a deficit, because I find him funny - it's just that having only one personality type in charge may begin to grate on certain people after a while).

So with that in mind I nominate the foll…

• ## Hyper-Alpha Notation Part III: Full Circle

March 7, 2018 by ArtismScrub

See parts 1 and 2.

This is it, the full generalization. I thought you guys said making a functional SGH-FGH map was hard!

Now, as you probably know, I generally do much better explaining notations through progression than through compact recursive rulesets. I have no idea how to put this one entirely into mathematical language. If this notation chokes at any point or the ordinals given are wrong, PLEASE tell me!

Anyway, this of course starts off with:

A ↑A A = A ↑b A

Now, my first idea was to go with ↑A+1 = ↑AA, but shortly afterwards I came up with a much better idea.

A ↑A↑ A.

Bam, A+1-level arrow.

This can continue with:

A↑↑ = A+2-level arrow

AA = A2-level arrow

AAA = A3-level arrow

And, of course, ↑AA = AA-level arrow. Easy!

This essentially means:

★…

• ## Pran - Powerful Repeating Array Notation

March 7, 2018 by BlauesWasser

Pran is a notation Is notation expressed as Pran.. (It looks more like a function.. I accidently wrote n instead of f)

Pran(10) = This image. Im using a link because I can't insert an image. Incase you didn't understand what n whould be like in the image. Just replace every 10 with n. (hopefully that is clear)

XD I guess that's enough to express it? If you have any questions, make sure to ask, and I will respond within a day.