• Nayuta Ito

    This is a parody of Dumb Ways To Die.

    Use infinity without care

    Give a cent to a illion-aire

    Prediction about the future date

    Use your private friends for evidence in debate

    Dumb ways to die, so many dumb ways to die

    Dumb ways to di-i-i-ie , so many dumb ways to die

    Remain your number with WIP

    And then you RIP

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  • Googleaarex

    Basicu matrix system is currently the 2nd fastest function that can be computed in the Googology with the notation-type expression. I like to thanks to PsiCubed2 to improve my encoding!

    There are 15 symbols being used in BMS:

    • ( and ) brackets (Groups of 2 symbols)
    • \(0^{40946385504}\) (Convert to unary, replacing it with the number to amount of 0s, 1-symbol system, end)
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  • Alemagno12

    There have been some new people joining the wiki lately, so I decided to make a series of blogs to help new people get started on googology. In this chapter, I will look at some of the mistakes that new googologists make.


    So you are new in googology, and you're trying to define a larger number than the current largest defined number, because that's what googology is about, right? One of the mistakes that some new googologists make is thinking that googology is about beating the largest number defined by defining a bigger one, or by defining the biggest number possible. But it's not only that: it's also about defining other large numbers, defining ways to define numbers, checking how large a large number is, checking how large are the nu…

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  • Mr. Junky

    Question about BEAF

    July 18, 2017 by Mr. Junky

    So I have had this question for a while.

    I know that {a,b,c} is a(b \(\uparrow\)s) to c

    But when it does something like {a,b,c,d) I have no idea how d affects this number. How exactly does d change {a,b,c}?

    Thus I have a question. In simple terms, how exactly do entries beyond the 3rd entry change the number being defined. We can do {a,b,c,d,e} but then how does e change {a,b,c,d) and we can do {a,b,c,d,e,f} but then how does f change {a,b,c,d,e} and so on? In arithmetic terms please.

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  • Googleaarex

    Aarex's Array Notation is my main notation I will use for large numbers. You can find the other extensions in my site.

    It is going to be original. I will never, ever stealing ideas.

    Simple AAN (sAAN) is the first extension of AAN. First, I will introduces the main rules and definition.

    I go with definition first. The people will say 'What is the definition' if I am going with main rules first.

    The definition of sAAN is a notation that expressed as a(A), where A is non-negative integers separated by the comma. The first entry is base and the second entry is co-base. The rest of the entries expressed as a hashtag and new copies of the group remain the same.

    • a(a,b,0) = ab
    • a()[d]

    If all of main rules doesn't apply, we start at the fourth entry in the p…

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  • Bubby3

    (0,0,0)(1,1,1) has level \(\psi(\Omega_\omega)\) 

    (0,0,0)(1,1,1)(1,1,0) has level \(\psi(\Omega_\omega+1)\)

    (0,0,0)(1,1,1)(1,1,0)(2,1,0) has level \(\psi(\Omega_\omega+\Omega)\)

    (0,0,0)(1,1,1)(1,1,0)(2,2,0) has level \(\psi(\Omega_\omega+\psi_1(0))\)

    (0,0,0)(1,1,1)(1,1,0)(2,2,1) has level \(\psi(\Omega_\omega+\psi_1(\Omega_\omega))\)

    (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0) has level \(\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))\)

    (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,2,0) has level \(\psi(\Omega_\omega+\Omega_2)\)

    (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,3,0) has level \(\psi(\Omega_\omega+\Omega_3)\)

    (0,0,0)(1,1,1)(1,1,1) has level \(\psi(\Omega_\omega*2)\)

    (0,0,0)(1,1,1)(2,0,0) has level \(\psi(\Omega_\omega*\omega)\)

    (0,0,0)(1,1,1)(2,1,0) …

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  • Bubby3

    The function types diverge at \(\Omega_2\)

    Here is the comparison.

    Function A Function B
     \(\psi(\psi_1(\Omega_2))\) \(\psi(\Omega_2)\)
     \(\psi(\psi_1(\Omega_2)+1)\) \(\psi(\Omega_2+1)\)
     \(\psi(\psi_1(\Omega_2)+\Omega)\) \(\psi(\Omega_2+\Omega)\)
     \(\psi(\psi_1(\Omega_2)*2)\) \(\psi(\Omega_2+\psi_1(\Omega_2))\)
     \(\psi(\psi_1(\Omega_2+1))\) \(\psi(\Omega_2+\psi_1(\Omega_2+1))\)
     \(\psi(\psi_1(\Omega_2+\Omega))\) \(\psi(\Omega_2+\psi_1(\Omega_2+\Omega))\)
    \( \psi(\psi_1(\Omega_2+\psi_1(\Omega_2)))\) \(\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))\)
    \(\psi(\psi_1(\Omega_2*2))\) \(\psi(\Omega_2*2)\)

    So the function catches up at \(\Omega_2*2\) and all multiples of \(\Omega_2\).

    I like Function B better because it is more extensible. 

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  • Mr. Junky

    I would like to define a few non salad numbers below to start here (I know how you guys feel about salad numbers).

    Basmati RICE: RICE[5](1000,100,10,10)

    RICEten: RICE[10](10,10,10,10)

    GoogolRICE: RICE[googol](googol,googol,googol,googol) Note: googol=10^100

    RICEplex: RICE[googolplex](googolplex,googolplex,googolplex,googolplex) Note: googolplex equals 10^googol, 10^(10^100) to simplify in just simple scientific notation.

    Would want to define larger but would be salad/transinfinite/hot mess. Eh what the heck.

    InfiRICE: RICE[infinity](infinity,infinity,infinity,infinity) a very powerful transinfinity, just for fun. Maybe even the smallest trans transinfinity!πŸ€”

    Also. I would like to give 1 very powerful quote from myself.

    "Any mathematical quantity c…

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  • Mr. Junky

    First welcome!

    July 13, 2017 by Mr. Junky

    I was searching for a long time a place to express my talent for large number making. I found this after a month or so when I came up with the idea to search for a large number wikia. I have been fascinated by your talents for months as a fandom user. Eventually I decided finally to stop shying away and join as a user. Would you please welcome me to your community? I also have some experience in googology from you guys. I know all about salad numbers, Rayo function, FOST, and so on. Also, I have past experience defining googological functions. One that has properties that allows it to be finite, infinite and transinfinite.

    Tetration Tower Notation:

    RICE function…

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  • Hyp cos

    What's the growth rate of Goodstein function? \(\varepsilon_0\)?

    No. Unlike Hydra function and Worm function, which are comparable to \(f_{\varepsilon_0}(n)\), Goodstein function has some "cost" - \(G(2\uparrow\uparrow n)\approx f_{\varepsilon_0}(n)\). By the definition of "functional approximation":

    \(f\ge^*g\) if there exists k such that for all n > 0, \(f(n+k)\ge g(n)\)


    \(f\approx g\) if \(f\ge^*g\) and \(g\ge^*f\)

    Goodstein function is not comparable to \(f_{\varepsilon_0}(n)\). Currently we don't have a compact notation to express the growth rate of it. However, in this blog post I won't consider this thing. Instead, I'll consider what it "costs" and extend it. Goodstein has a 3-level cost under \(\varepsilon_0\), since \(G(f_3(n))\app…

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  • Primussupremus

    The name of this number is Sindadrin-x. Its value in my notation is {10:↑((Ο‰^(Ο‰^2))(10)}.

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  • Primussupremus

    This is part 2: I will be starting at {K:↑(Ο‰+1)(X)} then moving on from there.

    {K:↑(Ο‰+1)(X)} = {K:↑(Ο‰)(X)} recursed ({K:↑(Ο‰)(X)}-1) times.

    {K:↑(Ο‰2)(X)} = {K:↑(Ο‰+Ο‰)(X)}= {K:↑(Ο‰+X)(X)} = {K:↑(Ο‰+X-1)(X)} recursed ({K:↑(Ο‰+X)(X)}-1) times.

    {K:↑(Ο‰3)(X)}= {K:↑(Ο‰2+x)(X)} = {K:↑(Ο‰2+X-1)(X)} recursed ({K:↑(Ο‰2+X-1)(X)}-1)times.

    {K:↑(Ο‰^2)(X)}= {K:↑(Ο‰*Ο‰)(X)}= {K:↑(Ο‰*X)(X)} = {K:↑(Ο‰*X-1)(X)} recursed ({K:↑(Ο‰*X-1)(X)}-1) times.

    {K:↑(Ο‰^Ο‰)(X)} = {K:↑(Ο‰^X)(X)}= {K:↑(Ο‰^X-1)(X)} recursed ({K:↑(Ο‰^X-1)(X)}-1)times.

    {K:↑(Ο‰^Ο‰+(1))(X)} = {K:↑(Ο‰^Ο‰)(X)} recursed ({K:↑(Ο‰^Ο‰)(X)}-1) times.

    {K:↑(Ο‰^Ο‰+(Ο‰))(X)} = {K:↑(Ο‰^Ο‰+(X))(X)} = {K:↑(Ο‰^Ο‰+(X-1))(X)} recursed ({K:↑(Ο‰^Ο‰+(Ο‰))(X-1)}-1) times.

    {K:↑(Ο‰^Ο‰+(Ο‰+1))(X)} = {K:↑(Ο‰^Ο‰+(Ο‰))(X)} recursed ({K:↑(Ο‰^Ο‰+(Ο‰))(X)}-1)times.


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  • Primussupremus

    In this post I will give you some examples for the notation I started to develop on my site Endless Possibilities,As well as a suitable/creative name.Some of the names are quite surreal so be prepared.

    Starting with the basics:{a}

    {100} = one hundred.


    {10,100} = 10^100 = one googol. {a,b,c}

    {10,10,10} = 10↑(10)10 = 10{10 up arrows}10 = Destratollion.


    {3,3,3,3} = tree-beardi

    {3,3,3,3,3} = triple-tree Moving on to {K&L}

    {6&5} = {5,5,5,5,5,5} = unarypenillion.

    {(4&4)&4} = tetragramattonillion.

    {((4&4)&4)&4} = hyper-tetragramattonillion.

    {100(100)100} = metatronillion.

    {25++:(12)} = Reindeer number.

    {25**:(12)} = super reindeer number.

    {34:↑(1)(29)} = the invincible king of doom.

    {5:↑(Ο‰)(6)} = {5:↑(6)(6)} = K-9 mark 2000,000.

    I'm not going to …

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  • Primussupremus

    This is (part of) the array of the Array notation I have started to define on  my site endless possibilities.

    {a} = a.

    {a,b} = a^b

    {a,b,c} = a↑(b c = a{b up arrow's}c

    {a,b,c,d} = {a,b,c} recursed d-1 times for d>1.

    for example:

    {3,3,3,3} = 3↑(3↑(3↑(3)3)3)3.

    In this way we can reach numbers like grahams number of {3,4,3,64} with ease.

    After thinking for a bit back when I first started developing this notation I decided to change things was I got to a 5 entry array and above.

    {a,b,c,d,e} = {a,b,c,d} recursed ({a,b,c,d}-1) times for e-1 repeats.

    With that I then defined k tuples or arrays of length>=5 to be:

    {k-1 tuple} recursed ({k-1 tuple}-1) times for the limit (entry/symbol)-1 repeats.

    As shown above: with {a,b,c,d,e}.

    Next I introduced a symbol & to …

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  • PsiCubed2

    I propose that people who are both:

    1. Rude and inconsiderate.

    2. Never contributed anything of worth to this community.

    Will no longer be given an absurd amount of leeway for their behavior.

    Newbies should be accepted with open arms. Brats who look for a place to vent their frustrations and insecurities - should not.

    Any veteran who agrees with me, please say so below so we can stop this from getting any worse.

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  • Bubby3

    I am continuing this page

    11^^3 takes up the rest of the skyscraper, which has 31 floors.

    12^^3 takes up 2 New York City rectuangular blocks (or 4 square blocks), or about 10 acres.

    13^^3 takes up a whole neighborhood of a big city, or about half a square mile.

    14^^3 takes up a whole city, or about 16 square miles.

    15^^3 takes up a 640 square mile city at New York City density, about the size of a county

    16^^3 takes up a 27,520 square mile city, which is between the size of West Virginia and South Carolina.

    17^^3 takes up about 1.2 million square miles.

    18^^3 takes up about 60 million square miles, or about the land area of the Earth

    o19^^3 takes up about 3 billion square miles, or about 10 star systems.

    20^^3 takes up the whole Local Bubble, or abo…

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  • Emlightened

    Mainly a discussion post. A TL;DR is provided at the end of each subsection of text, but please read through properly before commenting.

    Breakdown of classic definition of 'googology': We all (well, most of us) know what googology is, as a hobby. To quote the main page: "Googology is the mathematical study of large numbers, their properties, and their nomenclature."

    However, I don't think this is accurate, from either a hobbyist's or mathematician's perspective. In particular, large numbers don't have any natural noteworthy properties (known or theorised, afaik), aside from being above certain boundaries, and these are mostly pre-tetration.

    A natural nomenclature (system of naming, preferably scientifically) is possibly closer to hand, but this …

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  • Bubby3

    Mental torture.

    July 4, 2017 by Bubby3

    How to torture someone mentally! Make them imagine how big Graham's number is. Pertend an evil torturer is doing that to me

    Torturer: Try your best to visulalize these numbers. Let's expnlan up-arrow notation. Single arrows represent  exponentation. 3^3 is 27

    Me:Not very big.

    Torturer: Now double arrow is repeated single arrow, so a^^b is a^a...a^a with b a's

    Torturer: 3^^3 is 3^27 or around 7.6 trillion (explains how big a trillion is).

    Me:This is getting big!

    Torturer: Now let's introduce you to triple-arrows. Triple arrows are just repeated double-arrows, so  3^^^3= 3^^(3^^3) = 3^^(7.6 trillion). So you have a stack of exponents 7.6 trillion high. Let's show  you how big that is.

    Torturer: 3^^4 is 3 to the power of 7 trillion, or a number with…

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  • Benthe1st

    This is a WIP, so don't hate instantly XD This will be added to continuously.

    Also do tell me if i'm going about this right or wrong since i'm new. Hopefully this remake will make more sense. Also do tell me what needs to be clarified, as i know what im on about, but it is whether you know too.

    Also (again) do tell me what needs to be defined as like i have said, i dont know what you dont know about what im typing about.

    PLN = Previous Largest Number.

    || = Instead of using L for letter.

    (n↑↑↑) means an n amount of 3 up arrows. (E.g. A googol of 3 up arrows = googol↑↑↑)

    NOTE: If i dont explicitly state in a step to always sub in the largest possible value where possible then assume that it does anyway, it makes things easier this way.

    1.) Start with…

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  • Superman37891

    I would like to introduce a notation so obviously creative, and revolutionary that it will literally transform the definition of googology itself. It's special because the this notation becomes stronger as the functions and notations on here become stronger. Basically, no one will have to develop it, we all will unintentionally develop it. This is so funny that the annoying salad number fandom users are literally going to smash their devices in half, literally tossing stuff around their houses till it all breaks and the house breaks in half and their voice becomes all used up, for INFINITY!!! Why? Because they won't be able to spend 24 hours a day, 7 days a week ranting on here that we are defining salad numbers. Since they can't instantan…

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  • PsiCubed2

    The original list can be found here:

    For every number on that list I'll give here:

    (1) It's name.

    (2) The number written precisely in it's "home" notation (for example, Bowerisms are written in BEAF).

    (3) The number's Universal Canonical Form (for example 1000 = E3 and 2400 ~ E3.38).

    (4) The number's Binary Canonical Form (for example 2400 = 2.4E3).

    (5) The number's expansion into a lexicographic-ordered string (for example 2400 = E3-24).

    The table currently runs up to J10 = {10,10,10}. It will be extended shortly.

    Googolism Number UCF BCF LOS
    One 1 E0 1E0 E0
    Two 2 E0.3010 2E0 E0-2
    Three 3 E0.4771 3E0 E0-3
    Four 4 E0.6021 4E0 E0-4
    Five 5 E0.6990 5E0 E0-5
    Six 6 E0.7882 6E0 E0-6
    Ten 10 E1 1.0E1 E1
    Hundred 100 E2 1…

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  • Superraptor1234


    July 2, 2017 by Superraptor1234

    So I'm pretty new here, and to googology as a whole, but I'm just trying to get the hang of the ropes, while trying to avoid salad number type stuff. My goal is to come up with something of my own that is provably valid and then (hopefully) be able to prove where that falls into the current hierarchy (I'm not a mathematician by any means, I lean towards statistics more than anything, so a lot of this is most definitely guesswork (apologies in advance).

    Anyway, I have a word document I'm working on formatting for this page, so that others can critique it so I can better learn how to write mathematical proofs, that sort of thing. (Below I've included it as a gallery, with links to high-res imgur versions of those same photos). Please please p…

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  • QNw

    Subject Googology

    July 2, 2017 by QNw

    Welcome to my googology list. This is small list.

    Name Codename =
    Spyonclear Sector 0x005 Big Bukunukku Big Bukuwaha^20^Big Bukuwaha
    Spyonclear Sector 0x012 Meameamealokkapoowa surerb goomba Meameamealokkapoowa oompa^20^Meameamealokkapoowa oompa
    Spyonclear Sector 0x014 Lunnkhurn-1 Meameamealokkapoowa surerb goomba^20^Meameamealokkapoowa surerb goomba
    Spyonclear Sector 0x016 Lunnkhurn-2 Lunnkhurn-1^BIGG^Meameamealokkapoowa surerb goomba
    Spyonclear Sector 0x017x1 Lunnkhurn-3 Lunnkhurn-2^BIGG^Lunnkhurn-1
    Spyonclear Sector 0x017x2 Lunnkhurn-4 Lunnkhurn-3^BIGG^Lunnkhurn-2
    Spyonclear Sector 0x017x3 Lunnkhurn-5 Lunnkhurn-4^BIGG^Lunnkhurn-3
    Spyonclear Sector 0x026 Lunnkhurnbrot Lunnkhurn-150000000000000000↑↑↑↑↑↑↑↑↑↑↑↑↑Lunnkhurn-149999999999999999

    Name Code…

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  • Maxywaxy

    Hyper-N numbers

    July 1, 2017 by Maxywaxy

    i decided to do something off my blog cuz y not. here is what hyper N is:

    Hyper-N notation

    Gygul Series
    gygul=E100#^#100#^#100#^#100#^#100 gygulrex=Egygul#^#gygul#^#gygul#^#gygul#^#gygul gygulorex=E100#^#100#^#100#^#100#^#... with gygul 100s gyguldrex=En@n@n@n@n where n is gygulrex and @ is #^#
    Hyper-N notation (N#) Gy[a,b,c]=Ea@a@a@a... with b a's where @ is #^#^#^#... with C #s. gygul=Gy[100,5,2]
    gyngal=Gy[gygul,gygul,gygul] grand gyngal=Gy[gyngal,Gyngal,gyngal] Gyn(x)=Gy[x,x,x] bigrand gyngal=Gyn[grand gyngal]
    Gyn Function if n(x)=Gyn(Gyn(Gyn(Gyn(...Gyn(Gygul)...)))) where there is X Gyn(s Grangyn=n100 Greagyn=nnn...nnn100 with n100 n's. Gigyn=nnn...nnn100 with 'nnn...nnn100 with 100 n's' n's.
    Extended Hyper-N notation (+N#) if Grangyn=n100, Greagyn=n100,1…

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  • Hyp cos

    This kind of things have been discussed here.

    Currently, we have these size classes (in ascending order):

    1. Class 0 (< 6)
    2. Class 1 (6 ~ 106)
    3. Numbers with 7 to 21 digits
    4. Numbers with 22 to 100 digits
    5. Numbers with 101 to 309 digits
    6. Numbers with 309 to 4933 digits
    7. Numbers with 4933 to 1000000 digits (#3 ~ #7 are also called "Class 2")
    8. Class 3 (\(10^{10^6}\) ~ \(10^{10^{10^6}}\))
    9. Class 4 (\(10^{10^{10^6}}\) ~ \(10^{10^{10^{10^6}}}\))
    10. Class 5 (\(10^{10^{10^{10^6}}}\) ~ \(10^{10^{10^{10^{10^6}}}}\))
    11. Exponentiation level (\(10^{10^{10^{10^{10^6}}}}\) ~ \(10\uparrow\uparrow10\))
    12. Tetration level
    13. Up-arrow notation level
    14. Chained arrow notation level
    15. 5-6 entry linear array notation level
    16. 7+ entry linear array notation level
    17. Two row array notation level
    18. Planar array notatio…

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  • Primussupremus

    Here's a number I have defined from my site endless possibilities called Big 60:


    To understand how this number is derived I would like to refer you to the 1st two pages in my extremely large numbers series:

    When you are finished reading the required pages I would like to know what people think of Big 60.

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  • Primussupremus

    Here are some links to key googology pages on my website Endless possibilities hope you enjoy.

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  • Superman37891

    RICE function

    June 28, 2017 by Superman37891

    I would like to honor my Middle School Vice Principal Mike Rice as I leave him and move on to High School. So I got to thinking, and I thought what better way to do it than to name an extremely powerful fast growing function after him. Note: This is going to be the largest function I have ever defined, definitely bigger than FOOT AND Rayo combined. It is also finite, infinite and transinfinite at the same time. According to the definition of googology, because it is finite for finite inputs into it, it still counts as a googological function regardless of involving infinities and transinfinities at infinite and transinfinite inputs consecutively.

    The function RICE is defined below(Note: Sorry in advance for any confusion, I am trying my bes…

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  • Alemagno12

    Brain-Flak Challenge

    June 27, 2017 by Alemagno12

    Brain-Flak specification:

    There are only 8 valid characters that are accepted in Brain-Flak. If a code contains an invalid character, then the code is invalid. Start with two infinite stacks (left and right), which are a type of memory where elements can be pushed (add a number as the first element and move the rest of the elements down a stack) and popped (remove the first element and move the rest of the elements up a stack). The active stack starts at left. () evaluates as 1. (n) evaluates as and pushes n on top of the active stack. [] evaluates as the active stack height. [n] evaluates as -n. {} pops and evaluates as the top of the active stack. {foo} does foo until the number at the top of the active stack is 0, then evaluates as the … Read more >
  • Superman37891

    A large surprise

    June 26, 2017 by Superman37891

    Do you really want a ginormously large non-salad number? Yeah, well today I am going to give it to you. A number so large that no amount of googolistic competitions in the comments section could beat it, but could only approach it as the competition goes to infinity, and still be the exact same distance away from it. A number so large that multiplying it is meaningless to the value itself. The number is below. The almighty of all googolisms, reality, mathematics, spirit, and infinity! The unbeatable!

    THE NUMBER IS INFINITY!!!!!!!!!πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚πŸ˜‚

    {Note: The material below is intended as a joke and had no rude intentions in it's creation(Though you have every validity in perceiving it that way). Sorry for any content below that is …

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  • Milesman34

    This function is defined as 

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  • Milesman34

    So there are several numbers to define:

    Googolplexian is


    // Upper hyper operators function hyper(a, b, n): if n = 1: return a + b result := a repeat b - 1 times: result := hyper(a, result, n - 1) return result
    // Lower hyper operators function hyper_lower(a, b, n): if n = 1: return a + b result := a repeat b - 1 times: result := hyper_lower(result, a, n - 1) return result
    function dupleplex(a):
    if a = 1:
    return 10^10^10^100
    return dupleplex(a - 1) Read more >
  • PsiCubed2

    Are you okay with the situation on the mainspace right now, where people add more and more stub articles for obscure user-made numbers? Numbers which they don't even have something to say about?

    Because this is getting ridiculous. What's even more ridiculous, is that the wiki actually rewards the people who do so with badges and points (and I'm willing to bet that some people are doing this for the sole purpose of earning these points).

    In my opinion, the mainspace has turned into a complete farce. We should have actual notability criteria for numbers, and the main criteria should be "if a bot could have created the article you just wrote, it shouldn't be there in the first place".

    So, what do you think? Post your own opinion in the comments. …

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  • Primussupremus

    A few days ago I was experimenting with a new type of notation that is similar to BEAF but at the same time is vastly different,


    {a} = a.

    {a,b} = a^b

    {a,b,c} = a{b up arrows}c.

    {a,b,c,d} = {a,b,c} recursed d-1 times.

    To give an example of each of the 4 base levels we have:

    {3} = 3.

    {3,3} = 3^3 = 27.

    {3,3,3} = 3{ 3 up arrows} 3 =

    {3,3,3,3} = 3{(3{(3{3 up arrows}3) up arrows}3)up arrows}3.

    To make this a bit clearer here is a brief explanation using letters and numbers.

    Now that we have that defined we can move on to 5+ entry arrays.

    {a,b,c,d,e} = {a,b,c,d} recursed ({a,b,c,d}-1) times for n>0.

    Generally for an array of length k ( a k tuple) > 4 you recurse it ({k-1 tuple}-1) times.

    Now lets move on to using the array of operator in my array notati…

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  • Superman37891

    I have seen Primussupremus's first googolism defined using his notation, which gave me a great idea. I will define BIG FOOT Primussupremus.0 below using his notation. Note: This is just for fun, I already know that this is a salad and that it doesn't improve BIG FOOT by any significant amount.


    Edit: LOL, I have no idea how his notation works but I know it will easily beat his Ternarygollumtree. Credit for the array notation goes to Primussupremus.

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  • Superman37891

    I mean I already got that Rayo was the fastest growing function until 2014, only to be beaten by FOOT/FOST and nothing else as of today. I know that Rayo has some exotic stuff that gives it just the strength it has. I wanted to learn exactly how Rayo works, so I went to the page. But when I go to the explanation of the Rayo function, all I see is \(\phi \Psi \Theta \aleph \chi \delta \epsilon \Leftrightarrow \leftrightarrow \nabla \partial \eth \Im \Re \int \iint \iiint \iiiint\)\. And even wierder random stuff(I know that this notation will definitely not exist, just stated it to give an idea of how confusing Rayo is to understand based on the description of the Rayo function on the page Rayo's number). The only real thing I don't like is…

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  • Primussupremus

    This is the first official googolism defined using my notation {3,7,3| 3,7#3} = Ternarygollumtree number.

    I chose the name because it sounded kind of funny but also meaningful as gollum dies in the 3rd lotr book/film tree rhymes with 3 and Ternary is also related to the number 3.

    Later on I hope to create a stronger notation using an original extension to a BEAF style array that can produce some pretty phenomenal results.

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  • Nnn6nnn

    Since it seems hard to understand what's going on in the Googology Course, I am creating videos mimicking lessons for the course. You can find them here:

    I'm adding about 1 per week. It should take a few months to do everything for Googology I.

    Nathan Richardson "Simon Weston" 20:16, June 21, 2017 (UTC)

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  • Septexorgahepta


    June 20, 2017 by Septexorgahepta

    The gagfour is equal to \(A(4,4) = 2\uparrow\uparrow7-3 \text{~}10^{10^{10^{19728}}}\)

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  • Superman37891

    IQ Googological

    June 17, 2017 by Superman37891

    I would like to define IQ googological. It is the minimum IQ required to become an expert googologist. It is defined below using my Tetration Tower Notation.

    (Rayo's #, Rayo's #, Rayo's #,...)Rayo^Rayo^Rayo^Rayo^Rayo...^10^Rayo's# With Rayo's # Rayo's #s inside the brackets and Rayo's # Rayo(s) afterwards before ^10^Rayo's #

    Rayo's # just means Rayo(10^100) as originally defined as Rayo's # by Augustin Rayo

    My Tetrational Tower Notation explanation:

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  • Primussupremus

    Here is the rule set for my notation from: {a,b,c} to {a,b,c|d,k#p}

    [a,1,c] = a+c [a,2,c] = a*c [a,b,c] = a{b-2}c if c > 2 [a,b,c|0] = [a,b,c] [a,b,c|d] = [a,[a,b,c|d-1],c|d-1] [a,b,c|d,0] = [a,b,c|d] [a,b,c|d,e] = [a,b,c|[a,b,c|d,e-1]]

    Now on to {a,b,c|d,k#p}

    [a,b,c|@,0] = [a,b,c|@] (@ is any string) [a,b,c|@,p,q] = [a,b,c|@,[a,b,c|@,p,q-1]]


    [a,b,c|d,k#p] = [a,b,c|(p d's),k]

    So how do you think of that rule set.

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  • LittlePeng9

    Extending the hyperoperators to all real or complex values is a known open problem. Some time ago I had a somewhat converse idea on how to approach this - instead of starting with a fast growing function(s) on natural numbers and extending it to more inputs, we can directly construct a sequence of fast growing functions defined for all complex values. I do not claim this is of as much interest as extending hyperoperators, but might nevertheless be interesting for some.

    Suppose we have chosen a system of fundamental sequences for countable limit ordinals up to some bound. We now construct a sequence \(f_\alpha:\mathbb C\rightarrow\mathbb C\) which satisfies the following propertes:

    1. \(f_\alpha\) is an ,
    2. \(f_\alpha(z)\in(0,\infty)\) for \(z\in\m…
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  • Bubby3

    Everything up to w^^(w^2) is from Sbiis Sabian's examples.

    w^^(w^2+1)= phi(w,0) = w^^(w^w) in Saibain's example.

    It is too complicated to exmplain. I don't know how it works between w^^(w^2) and w^^(w^2+1), but here is a guess. 

    We now invent the >> operator. (#^^##)>>#= #^^### in Saibian's current system. Here are some comparisons,

    (#^^##)>>(#+#)= #^^####


    1. ^^### = #^^^#

    (#^^###)>># = #^^^##

    This gets really complicated

    By w^^(w^w), we are already at BHO. This is strong.

    w^^^3, or w^^(w^^w) has level W_w.

    w^^^w is as strong as Bashicu matrix system and we are only at pentation. This is very strong.

    I don't know how the higher hyper-operators work.

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  • Superman37891

    Welcome to Rayo's Attempt The Sequel!

    I need to define a few things first though(I don't know how to do subscript, I will use [n] instead to replace subscript]

    Start from Rayo[1] which is just Rayo's function 1 time

    Rayo[n]^x(Y) is Rayo[n] iterated x times to y

    Rayo[n+1]^ assumes Rayo[n+1] is Rayo[n] iterated Rayo(10^100) times

    So now I will start

    Let's set Rayo[googolplex](10^100) equal to JASON(best thing I could come up with)

    Rayo[JASON](10^100) is equal to POLLUTION (This number is LARGE, as it is supposed to represent the evil of pollution to 🌏 when it was tricking the public into developing it to destroy earth and be dependent on it)

    Rayo[POLLUTION](10^100) is equal to DISPOSAL AND RENEWAL (The number representing how much good we could do f…

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  • Koteitan

    Here is new SNS for talking about Googology!


    Googoldon is a twitter-like SNS in which Mathjax is available. I want to make this site global, so any languages will do in this site. Any type of discussions, ideas, questions, monologue will do. Please try it!

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  • Primussupremus

    After being away for quite a while from the wiki I decided to come back and try and create a better rule set for my notation starting at {a,b,c}.

    I will first show them examples then develop a rule set from that.

    {a,b,c} = {a (b-2 up arrows c}

    for: b< 3 = a*b for b= 2 and a+b for b=1.

    If  b >= 3 apply the rule in line 1.

    Now that I've got the rule set down for {a,b,c} I can start to give some examples:

    {1,1,1} = 1+1 = 2.

    {2,2,2} = 2*2 = 4.

    {3,3,3} = 3^3 = 27.

    {4,4,4} = 4(2 up arrows) 4.

    {5,5,5} = 5( 3 up arrows) 5.

    {6,6,6} = 6( 4 up arrows) 6.

    {7,7,7} = 7(5 up arrows) 7.

    {8,8,8} = 8(6 up arrows) 8.

    {9,9,9} = 9(7 up arrows) 9.

    {10,10,10} = 10(8 up arrows)10.

    Now that I have given some examples I will write down a unique name for each of these examples:


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  • SandstoneGem

    x|y - means x^10^y! where x and y are numbers

    [x] - means x^10^x^10

    {x} - means [x] * [x]

    L - means LOWER LAYER - {x} ^ {x}

    M - means MEDIUM LAYER - L! * {x{x{x}x}x}

    H - means HIGHTER LAYER - M! ^ M!

    S - means HIGHTEST LAYER - (((H!)!)!)!

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  • Superman37891

    I am deciding to define a number as a thank you to a friend of mine for something he did today. PARKER WOLF THE HULK defines the athleticism of my friend Parker Wolf. Note that I got permission from him and that it uses my Tetration Tower Notation.

    (9999999999999999,99999999999999,9999999999999,9999999999999,9999999999999,99999999999999,99999999999999,99999999999999,99999999999999,99999999999999... with 9999999999999999 (99999999999999's)) 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

    Note: I know that this is a very complex extension, I jus…

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  • Superman37891

    I want to get your feedback on defining an extended version of the Rayo function. I want to try something, and you can tell me simple ways to make it larger if you want. Just is you know, yes, I do know that it is using another predefined function, but I also want to see whether it is still a salad number or not. It is defined below


    Keep in mind, yes, I had to try very hard to not use any predefined numbers, if I would have my number would have been so much larger, though some tiny simpler tweak could beat it since Rayo is so strong it can destroy the entire Omniverse.

    Based on PsiCubed2's comment and my confirmation, I have edited the definition to simplest form. When I say Rayo^200,000, I do mean that it is Rayo's f…

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  • O.murphy.b.123

    Today I created a sequence of numbers called the Bektelsson Exponential Triangle Sequence (or BExTr[]) In this sequence BExTr[a] = the first a triangular numbers ^^^^... ^^^ to each other in which there are a - 3 arrows.

    The number 1 is not considered a triangular number in this function, because that would lead to an infinite loop of ones

    For example, BExTr[1] = 3

    BExTr[2] = 3 + 6 = 9

    BExTr[3] = 3 x 6 x 10 = 180

    BExTr[4] = 3 ^ 6 ^ 10 ^ 15

    BExTr[5] = 3 ^^ 6 ^^ 10 ^^ 15 ^^ 21

    BExTr[6] = 3 ^^^ 6 ^^^ 10 ^^^ 15 ^^^ 21 ^^^ 28

    And so on.

    I have created the suffix -suuri, so that a-suuri = BExTr[a]

    Tensuuri = BExTr[10]

    Hundredsuuri = BExTr[100]

    Thousandsuuri = BExTr[1000]

    BExTr[googol] = googolsuuri = schmoogol

    Bischmoogol = BExTr[schmoogol]

    Trischmoogol = BExTr…

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