Hyper X notation
This notation is used to make large numbers like most other notation like hyper E notation(ExE)
X10= 10{10}10 (Tridecal)
Xn= n{n}n
XXn=n{Xn}n
Xn#m=XX.....(m X's)XX.....((m-1)X's)..................................XXX(3 X's)XX(2 X's)X(1 X)n
Xn#m#y=Xn#(Xm#y)
Xn##m=Xn#n#n#....n(m #'s)
1.Xn=10(n=0), Otherwise Xn= n{n}n
2.XXn=20(n=0), Otherwise Xn= n{n}n
3.Every X(s) that you add in the front when n=0, you add 10
4.Xn#m=X10(n,m=0),Otherwise Xn#m=XX.....(m X's)XX.....((m-1)X's)..................................XXX(3 X's)XX(2 X's)X(1 X)n
Xn{1}m=Xn#m
Xn{2}m=Xn#m
Xn{#,1}m=Xn{Xn{n+m}m}m
Xn{#,2}m=Xn{Xn{Xn{n*m}m}m}m
Xn{#,3}m=Xn{Xn{Xn{Xn{n^m}m}m}m}m
Xn{#,4}m=Xn{Xn{Xn{Xn{Xn{n^^m}m}m}m}m}m(add one ^)
Xn{#,#}m=Xn{#,m}=Xn{Xn{Xn{Xn{Xn{Xn.....n{(m-2)}m.....m}m}m}m}m}m
Xn{#,#,#…
(2021-10-23) New Policy
This article was written in Japanese and will be translated into English later.
私は、今、このウィキのポリシーを書き直しています。
まず、私は、ポリシーとガイドラインの役割分担を明確にしたいです。今のポリシーは複雑になりすぎています。
次に、私は、 Googology Wiki のブログの投稿をソースに用いることを全面的に解禁した方がよいと考えています。これは自作の巨大数の記事を作成することを阻止するための制限でしたが、 Google Site などにより簡単に回避されてしまっています。それならば、ブログの投稿をソースに使えるようにすることで、他の人によるブログの投稿での反論を記載できるようにした方がいいと思います。また、 Google Site などの個人サイトは変更をキャッチすることが難しく、いっそのこと全面的にブログの投稿だけをソースに使えるようにした方がいいのではとも思っています。
次に、私は、 Voting は必要性を感じないので削除しようと考えています。その代わりに、投票の方法についてのガイドラインを設定する方が良いのではないでしょうか。
unnamed factorial
im bad at extending this to make it sound "formal" so i will just dump the definition
Notated as: (not so good approximation) E25#539
5? = no idea how to calculate
any sugestions to how i shall name this? i have considered interrogatorial (or ?torial) and detonatorial (detonate + factorial, kinda obvious), i also thought of making it the fourth superfactorial, since it beats all of them
edit: i dont think i wanna name it detonatorial, so either i name interrogatorial (or ?torial) or i make a superfactorial
Sushi number🍣🐠🐡
One of the world's biggest numbers, dedicated to one of the world's best foods! My attempt at making the largest valid googologism. Leave any corrections in the comments, and I will make sure to fix them because I won't let a tiny mistake get in my way :)
I guess I could keep going, but I'm fine with stopping now. Hopefully the fourth sushi number is the largest valid googologism :)
Is this correct?
Today, I will do a good meaning towards E# and xE#
E A=10^A
A E B=A*10^B (following rules of equations...)
E A#B=E (E A#(B-1) )
E A#B#C=E A#E (A#B#(C-1))
? will now mean unknown part of txt.
E ?#X#Y = E ?# E ?#X#(Y-1)
E X##Y = E X#(X##(Y-1))
E X##1 = E X
E X #^{Y} Z=E X #...# Z Y #'s { because i hate writing ##########################################}
E X#^{Y}Z=E X#^{Y-1}X#^{Y-1}......X#^{Y-1}X#^{Y-1}X Z X's
GODGAHLAH= E 100#^{100}100
that all
Idea for CNF-based large function
We assume the reader is familiar with Cantor normal form. This is inspired by Michael Rathjen's coding function in the Art of Ordinal Analysis. We define a coding function \(\textrm{wCNF}: \omega^\omega \mapsto \mathbb{N}\) like so:
- \(\textrm{wCNF}(0) = 0\)
- If \(s =_{CNF} \omega^{s_1} + \omega^{s_2} + \cdots + \omega^{s_n}\), \(\textrm{wCNF}(s) = 2^{s_1 + 1} + 3^{s_2 + 1} + ... + p_n^{s_n + 1}\), where \(p_n\) is the \(n\)th prime number.
Due to the use of prime numbers, most outputs will be unique (not all sadly), and some outputs will never appear.
\(\textrm{wCNF}(0) = 0\)
\(\textrm{wCNF}(1) = 2^{0+1} = 2\)
\(\textrm{wCNF}(2) = 2^{0+1} + 3^{0+1} = 5\)
\(\textrm{wCNF}(3) = 2^{0+1} + 3^{0+1} + 5^{0+1} = 10\)
\(\textrm{wCNF}(\omega) = 2^{1+1} = 4\) …
There's PTOs, why not MTOs?
As you all probably know, the proof-theoretic ordinal of a theory T is given by the following formula:
\(||T|| = \textrm{sup}\{\textrm{otyp}(\prec) | \prec \textrm{is} \; \textrm{a} \; \textrm{primitive-recursive} \; \textrm{well-ordering}; T \vdash TI(\prec)\}\).
Well, I suggest the model-theoretic ordinal, which is given by the following formula:
\(MTO(T) = \textrm{min}\{\alpha: L_\alpha \models T\}\) and \(MTO_2(T) = \textrm{min}\{\alpha: L_\alpha \cap P(\omega) \models T\}\)
For most theories, I believe that the MTO is greater than the PTO.
I'm not sure about MTO(PA), but I think it is \(\omega\).
\(MTO(KPi) = MTO_2(\Delta^1_2 - CA + BI) = MTO(KP +\) there exists a transitive collapse for any well-founded relation\()\) is the first recursive…
Making Salad
Lettuce, Pineapples and Cucumbers
(THESE NUMBERS WERE WRITTEN FROM SMALLEST TO LARGEST, IF THERE IS ANY PROBLEM, PUT IT IN THE COMMENTS)
(SOME OF THIS NUMBERS ARE ILL-DEFINED)
(I WILL UPDATE THIS PAGE LIKE A GOOGOL TIMES, COME HERE AGAIN WHEN YOU WANT TO EAT SALAD)
- 1 Googol and Decker
- 2 Goshomity
- 3 Meameamealokkapoowa
- 4 TARANOVSKY and LOADER
- 5 W H Y ?
- 6 REAL EXTENSIONS
- 6.1 Oblivion Extensions
- Googoltriminex, 10-(101010100)
- Googolduminex, 10-(1010100)
- Googolminex, 10-(10100)
- Tri-Little Googol, 0.08100
- Bi-Little Googol, 0.4100
- Bi-Little Googolplex, 0.40.4100
- Unker, 1
- Bker, 4
- Trker, 7625597484987
- Little Googol, 2100
- Googol, 10100
- Googolduteen, 10100+20
- Googoltriteen, 10100+30
- Googolquadriteen, 10100+40
- Googolquinteen, 10100+50
- Googolcentiteen, 10100+100
- Googolty, 10101
- Googolt…
Analysis of galaxy function
\(\iota(0) = \textrm{Galaxy}(0, 1) = \$\omega\)
\(\iota(1) = \textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0))\)
\(\iota(2) = \textrm{Galaxy}(\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0)), \textrm{Collapse}_{\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0))}(0))\)
\(\iota(3) = \textrm{Galaxy}(\textrm{Galaxy}(\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0)), \textrm{Collapse}_{\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0))}(0)), \textrm{Collapse}_{\textrm{Galaxy}(\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0)), \textrm{Collapse}_{\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0))}(0))}(0))\)
\(\kappa(0) = f_{\textrm{Galaxy}(\$\omega, \textrm{Collapse}_{\$\omega}(0))}(2)\)
\…
Galaxy function
This is an ordinal notation I developed, partially inspired by Taranovsky's C. I wanted to play around and test out some different ideas and combine them into one. Put any errors or criticism in the comments.
- 1 Overview
- 2 Notation
- 3 Relation
- 4 Standard form
- 5 Cofinality & Fundamental Sequences
- 6 FGH
I was listening to this really cool song called Galaxy Collapse and I thought it would be cool to name a function after, also Galaxy Collapse and Ordinal Collapsing Function share the word "Collapse" although this isn't an OCF. Anyway:
Here, I will define the character string for the notation:
- \(0 \in T\)
- For all \((a, b) \in T^2\), \(a+b \in T, PT\)
- For all \(a \in T\), \(\textrm{Scream}(a) \in T, PT\)
- For all \((a, b) \in PT \times (T \backslash \{0\})\), \(\t…
Journey to Infinity: Part 1
Hello everyone! This is Avem231, and welcome to the first part of Journey to Infinity, a resurrection of the Hunt for the Largest Number series that never caught on. Unlike in the previous series, where I simply made an ill-defined salad function, this time, I will actually try to create a clear definition for the googolisms I will be making along the way. Without any further ado, let's begin!
In Sbiis Saibian's explanation of the Fast-growing hierarchy, he left off with Γ0 as the largest possible ordinal you can plug into f. Because of this, I will be making my own extension of the FGH that picks up from where he left off, and goes even further beyond with the already-insane potential of the hierarchy.
There are a lot of infinitely nested power…
My SI Prefixes Extensions
MADNESS STARTS NOW
Value
-∞
1
0.5
0.33333...
0.25
0.2
0.16666666...
1/7
0.125
0.11111111...
1/11
1/12
1/13
1/14
1/15
1/16
1/17
1/18
1/19
1/20
1/21
1/22
1/23
1/24
1/25
1/30
1/50
1/90
Value
10-27
10-30
10-33
10-63
10-93
10-123
10-153
10-183
10-213
10-243
10-273
10-303
10-3003
10-30003
10-300003
10-3000003
10-30000003
10-300000003
10-300000003
10-3000000003
10-(3×1012+3)
10-(3×1015+3)
10-(3×1018+3)
10-(3×1021+3)
10-(3×1024+3)
10-(3×1027+3)
10-(3×1030+3)
10-(3×1033+3)
10-(3×10303+3)
10-(3×103003+3)
One of my array notations: SSAN (superspeedy)
I created this. It's quite powerful, though not very accurate because it's based on FGH not hyperoperators (exponentiation, tetration, etc). However, it is very powerful: I might be able to snag SAN's title if I try hard enough.
NOTE: I only just realised that there exists an SSAN, hopefully I can change its name somehow.
Instead of adding some rules for 2-ary and 3-ary, then adding recursion, I will add unique rules for each array length, and if they get large enough I will switch to recursion, which is probably not as powerful.
\(SS\{a, b\} = f_b(a)\), so \(\{n, 4\}\) is on par with tetration
\(SS\{a, b, c\} = f_{\varphi(c, b)}(a)\) using fundamental sequences for the Veblen function, so \(\{n, 0, 1\}\) is on par with Kirby-Paris hydras
\(SS\…
Judy's Number
Judy's Number is a HUGE number written in Judy's function that is based off of Knuth's up-arrow notation, and is similar to Graham's function. It's based off of some random person named Judy and her favorite number 7.
You start with 7↑↑↑↑↑↑↑7 ( with 7 arrows) that is J1 in Judy function 7{7}7 in BEAF or a Trisept
J2 = 7↑↑…↑↑7 (with J1 arrows) or 7{7{7}7}7 in BEAF
J(n) = 7↑↑…↑↑7 (with J(n-1 ) arrows)
Judy's Number = J7 = 7↑↑…↑↑7 (with J6 arrows) 78 in BEAF
Judy's Number is \(f_{\omega+1}(7)\) in the Fast-growing hierarchy
Little Graham is bigger than it because it starts with 2↑↑↑↑↑↑↑↑↑↑↑↑3
J(n) grows faster than G(n) because J(n) starts with 7↑↑↑↑↑↑↑7 while G(n) start with 3↑↑↑↑3
the augmentation function
came up with on a night just doing weird things casually:
So first of all, this function doesnt use numerical, it takes operations itselves:
Basically: , passing it through the augmentation function would increase every hyperoperator, so A_1() = 5^^^^^^5. It also works with operations with more hyperoperators, lets say (8^8)^^^3, A_1() = (8^^8)^^^^3, and there is more, A_2(5^^^^^5) = 5^^^^^^^5, as you notice, A_n(m^m) = m^^^ . . (n number of arrows) . . ^^^m, as i said earlier, It also works with operations with more hyperoperators, A_10(8^7^6) = 8^^^^^^^^^^^7^^^^^^^^^^^6.
Si function 四
My second notation thingy (not sure what it classifies as). Hopefully it will be well-defined this time.
Thanks to Kanrokoti, P-adic
Parts of this were copied from Kanrokoti's non-restricted 三 function because I'm sorta lazy, go check out the original here.
- 1 Notation
- 2 Relation
- 3 Cofinality
- 4 Fundamental sequences
- 5 Fast-growing hierarchy
- 6 Fast-growing function
- 7 Normal form
Here, I will define the character string which I will use for defining the notation. I define two sets \(T\) and \(PT\) of formal strings consisting of \(0\), \(\textrm{四}\), \(+\), \((\), \()\) and commas in the following recursive way:
- \(0 \in T\).
- For any \((a, b) \in T^2\), \(\textrm{四}_a(b) \in PT \cap T\).
- For any \((a_1, a_2, ..., a_m) \in PT^m\) such that \(2 \leq m < \infty\), …
My notation
10^5=[10,5]
10^x=[10,x]
10^10^100=[10[10,100]]
10^10^x=[10[10,x]]
10^^100(10{2}100)=[10,2,100]
10{x}y=[10,x,y]
[10,3[10,2[10,2[10,172]]]]=10^^^10^^10^^10^172
PEGG entered The Eon Of Undefined
Can anyone delete this article? I found that Q is complete before September 19th.
LaTeX testing blog: just scroll away
I will just use this blog for testing random LaTeX stuff. This blog will likely grow in length over time xD
\(\textrm{四}\)
Explaining Numbers That I Named xd
I ONLY GONNA EXPLAIN THE NUMBERS FROM HERE https://googology.wikia.org/wiki/User_blog:GerfloJoroZ/Every_Number_that_i_(tried_to)_name.
WARNING: idk
- 1 Sammy
- 2 Undertale C1
- 3 Undertale C2
- 4 Undertale C3
- 5 Undertale C4
- 6 Undertale C5
- 7 Undertale C6
- 8 Undertale C7
- 9 Undertale C8
- 10 Undertale C9
- 11 Undertale C10
- 12 Grabielplex
- 13 Gaxalogue
- 14 Supalogue
- 15 Versalogue
- 16 Multalogue
- 17 Multataxis
- 18 Borcal
- 19 Megaham
- 20 Megorcal
- 21 Multaham
- 22 Multorcal
- 23 Loud, Bi-Loud and Tri-Loud Multorcal
- 24 Multintar
- 25 Hekto-Multintar
- 26 Multo-Multintar
- 27 Randomgirlwanttohavesexwithme-illion
- 28 Ultrafour
- 29 Ultrafourplex
- 30 Ultrasam
- 31 Ultrasamplex
- 32 Gerflo's Number
- 33 Gerflillion
- 34 Ultragerflo
- 35 Ultragerfloplex
Biggest negative undescribable number.
The number of original Undertale AU's (13 Jun 2021)
The number of Undertale AU's …
Situation around BIGG
For years it was considered as one of the largest numbers ever existed. I even wrote somethere that it was around {L,X,2}200,200 in BEAF. Now that BEAF at this level is possibly well-definable (but it is clearly ill-defined for now) and first rule is to create 200 pairs of brackets by following recursive rule: {L,X,2}[1] = L and {L,X,2}[a+1] = {L,{L,X,2}[a]} (it requires expansion of L into 200-part &-chain, though) but for BIGG even first rule is not clear. So my previous statement that n? is about f_{ψ_{χ_0(0)}(ψ_{χ_1(0)}(0))}(n) in Rathjen's "small psi" function is meaningless.
n(k) calculator
I created a calculator to calculate n(k) here a while back:
https://www.khanacademy.org/computer-programming/nk-calculator/4781994459938816
It uses the tree building method to calculate n(k), aka calculating all strings of a certain length that work, which I think is the fastest method to calculate n(k). It correctly calculates n(1) and n(2). Recently I optimized the code which cuts the run time quite a lot. However, I was still unable to perform the calculation process for n(3) beyond length 9 due to KA's infinite loop protection, which I was unable to get rid of.
Any ideas on how to improve the program?
Also, if there was no infinite loop protection, will the number of valid sequences for a certain length grow googologically large, or will t…
WORLD WIDE -ILLIONS
FANMADE -ILLIONS
- Micresillion: 10(3×(103×(1)+3)+3
- Shelillion: 10(3×(103×(2)+3)+3
- Samonillion: 10(3×(103×(3)+3)+3
- Marhsisillion, Vanutanillion: 10(3×(103×(4)+3)+3
- Palaunillion: 10(3×(103×(5)+3)+3
- Occiharillion: 10(3×(103×(10)+3)+3
- Soloislillion: 10(3×(103×(20)+3)+3
- Vaticitillion: 10(3×(103×(27)+3)+3
- Sapiminillion: 10(3×(103×(31)+3)+3
- Montserrillion: 10(3×(103×(33)+3)+3
- Macanosillion: 10(3×(103×(63)+3)+3
- Malvisnillion: 10(3×(103×(1367)+3)+3
- Barthillion: 10(3×(103×(1548)+3)+3
- Sacrynievillion: 10(3×(103×(1762)+3)+3
- Neerlandillion: 10(3×(103×(1998)+3)+3
- Butanillion: 10(3×(103×(2559)+3)+3
- Isvirbrillion: 10(3×(103×(2642)+3)+3
- Antibarbillion: 10(3×(103×(2815)+3)+3
- Turcaillion: 10(3×(103×(2824)+3)+3
- Sanvylagrillion: 10(3×(103×(3158)+3)+3
- Dominicillion: 10(3×(103×(3197)…
Well... Eightanoards flushing
So Sussylion is so big number bcs is sus :flushing:
One sussyllion ecuals 10^(3*(101001↑↑↑110^1010^101^1010011)+3) bcs from binary code 1010011 1010101 1010011 - SUS
And next is SUSSYBAKALLION
So... Im dumb.... Well Sussybakallion - 10^(10^(3*(101001↑↑↑110^1010^101^1010011)+3)) :flushing:
Next number will be... VERY BIG... Big... Bi... Oh no... Now its your chance to ba a flushing: A...
Gerflojoroznaon - Virusgayniard^Sussybakallion^(Undertale C10*Underfell C8)
And
Gerflojoroznaod - Gerflojoroznaon↑↑↑↑↑↑↑Gerflojoroznaon*Sussybakallion :flushing:
Well... It was my stoopid blogpost
Now i will eat chocolate bcs im not playing in gayshit infart
:flushing:
This Ordinal thing I made
I made this ordinal collapsing function , where y is a positive integer.
LOUD
LOUD > FORCE > GRAHAM
- 1 HOWWWWWWWWWWWWWWWWWWWWWWWW
- 1.1 Forcal
- 1.2 Borcal
- 1.3 Decorcal
- 1.4 Megorcal
- 1.5 Multorcal
- Forcal: G1(1000000)
- Force Forcal: G2(1000000)
- Bi-Force Forcal: G3(1000000)
- Tri-Force Forcal: G4(1000000)
- Loud Forcal: G1(1)
- Bi-Loud Forcal: GG1(1)(1)
- Tri-Loud Forcal: GGG1(1)(1)(1)
- Borcal: G2(1000000)
- Force Borcal: G3(1000000)
- Bi-Force Borcal: G4(1000000)
- Tri-Force Borcal: G5(1000000)
- Loud Borcal: G2(2)
- Bi-Loud Borcal: GG2(2)(2)
- Tri-Loud Borcal: GGG2(2)(2)(2)
- Decorcal: G10(1000000)
- Force Decorcal: G11(1000000)
- Bi-Force Decorcal: G12(1000000)
- Tri-Force Decorcal: G13(1000000)
- Loud Decorcal: G10(10)
- Bi-Loud Decorcal: GG10(10)(10)
- Tri-Loud Decorcal: GGG10(10)(10)(10)
- Megorcal: G1000000(1000000)
- Force Megorcal: G1000001(1000000)
- Bi-Force Megorcal: G1000002(1000000)
- Tri-…
Every Number that i (tried to) name.
I GONNA DIE. (Salad Numbers Almost Everywhere)
- Sammy: S(-1), The biggest finite undefinable negative number
- Undertale C1: 1372
- Undertale C2: 1882384
- Undertale C3: 3543369523456
- Undertale C4: 35433695234562
- Undertale C5: 35433695234564
- Undertale C6: 354336952345616
- Undertale C7: 354336952345665536
- Undertale C8: 3543369523456265536
- Undertale C9: 35433695234562265536
- Undertale C10: 354336952345622265536
- Gabrielplex: 10Gabriel's Number
- Gaxalogue: 10↑↑(103×1033)
- Supalogue: 10↑↑(103×1036)
- Versalogue: 10↑↑(103×1039)
- Multalogue: 10↑↑(103×1042)
- Multataxis: 10↑↑↑(103×1042)
- Baham: G2(64)
- Borcal: G2(1000000)
- Decaham: G10(64)
- Decorcal: G10(1000000)
- Megaham: G1000000(64)
- Megorcal: G1000000(1000000)
- Multaham: G(103×1042)(64)
- Multorcal: G(103×1042)(1000000)
- Loud Multorcal: G(103×1…
A system utilizing uncountable ordinals better than OCFs?
Hi, first post. So this idea came to me as I was messing around with ordinal notation, being inspired by Stephen Brooks's transfinite number line, which was recently updated to include ordinals up to BHO. The concept is to ditch the multiple arguments of the extended Veblen function and instead use ). Again, if you have some sources for reading, do share them.
Weak K-psi function
Japanese version: https://googology.wikia.org/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Kanrokoti/%E5%BC%B1K-%CF%88%E9%96%A2%E6%95%B0
- 1 Overview
- 2 Weak K-psi
function
- 2.1 Notation
- 2.2 Ordering
- 2.3 Cofinality
- 2.4 Search function
- 2.5 Fundamental sequence
- 2.6 FGH
- 2.7 Standard form
- 2.8 Naming
We define Weak K-psi function. This notation extends Ordinal Notation Associated to Extended Buchholz's OCF.
Special thanks: p進大好きbot
Let \(T\) and \(PT\) are sets of formal strings consisting of \(0\), \(+\), \(\psi\), \((\), and \()\), which are simultaneously defined in the following recursive way:
- \(0 \in T\).
- For any \((a,b) \in PT \times (T \setminus \{0\})\), \(a+b \in T\).
- For any \((a,b) \in T^2\), \(\psi_a(b) \in PT \cap T\).
\(0\) is abbrevi…
Formalized and fixed plus notation
Plus notation is a notation with correspondence to ordinals which I developed. In this blog post, I will be formalising and fixing it. Note that here, I only use ellipses in a case such as \(\lbrace a_0, a_1, ..., a_n \rbrace\) to show a set with \(n+1\) elements. I say this to avoid ambiguity. So, without further ado, let's jump right into it!
We work in a set \(\Sigma\) of symbols: \(+\), \(0\), \((\), \()\), \(*\), \(\textrm{^}\), \(\langle\), \(\rangle\) and \(/\). The set \(\Sigma*\) is the set of formal strings consisting of symbols from \(\Sigma\).
We define a set of valid formal strings \(OT\) (i.e. a subset of \(\Sigma*\)) like so:
For a formal string \(S \in \Sigma*\), \(S \in OT\) if it satisfies all these requirements:
- It is non-em…
blog post
I define (n) as the largest number which is the output of a Turing machine which has n non-limit non-halting states, except when the machine tries to move to the left of its starting point, it halts.
Fast-growing combinatorial function I made because I was bored
This is a fast-growing combinatorial function.
- 1 Rules
- 2 BCF(0)
- 3 BCF(1)
- 4 BCF(2)
- 5 BCF(3)
- 6 BCF(4)
- 7 BCF(5)
- 8 BCF(6)
- 9 List of early values and
comparison to \(\Sigma(n)\)
- 9.1 BCF
- 9.1.1 vs.
- 9.2 BB(n)
- 9.1 BCF
Start with S0 = 0. Then increase it by the following rules:
Sx+1 = 0(S0S1S2...Sx)
For example, S4 = 0(S0S1S2S3) = 0(00(0)0(00(0))). You calculate BCF(n) like so:
Take Sn and reduce it by the following rules:
0A => A
00A => 0
000A => 0A(0A)
Take the amount of steps that reducing until you reach 0 took, and label it as BCF0(n). Then to compute BCFx+1(n), take a string of BCFx(n) consecutive zeroes and count how many steps it took to reach 0 = 3 * BCFx(n). BCF-(n) = BCFBCF0(n)(n) = BCF0(n) * 3^BCF0(n). BCF(n) = BCF0(n) * 3^(BCF0(n) * 3^(..BCF0(n) * 3^BCF0(n))) with BCF0(n) ste…
Creating a pointless fast-growing function via recursion on the TREE and weak tree functions
Pretend this blog post doesn't exist.
"Mini OCF - Pt. 2"
So, normal OCFs collapse down uncountables to return countables, and this "mini OCF" collapses countables to return finite numbers. Therefore, I guess it's more of a googological notation then ordinal notation or collapsing function. I have created 3 previous mini OCFs, and this article will be about my newest, most powerful and most extensible. This is the first part of TMOAN. For the full version and any future updates, see here.
Thanks: User:Username5243, User:P進大好きbot, User:Denis Maksudov, User:Kanrokoti
- 1 Pre-Alpha Stage
- 1.1 I: Stage 0
- 1.2 II: Stage 1
- 1.3 III: Linear
Pre-alpha stage TMOAN covers from basic to nested arrays.
Stage 0 is the lowest level of TMOAN. It involves no infinite ordinals in the expression. Basic TMOAN consists of the follo…
Testing Blog
I Just Made This Blog So That I Could Experiment with Latex and make functions with it the stuff, just scroll away.
generalizes w+n, makes 2w and adds it to the list.
array notation idea thing
so basically i came up with this like yesterday, still have no idea how tf i came up with it (sorry if some things are horribly badly explained)
{a} =
Anything(~^b)a = Anything(~^b-1)Anything(~^b-1)Anything . . . Anything(~^b-1)Anything(~^b-1)Anything
thats all i guess
More illions\
Define t$A,B = Bth tier A illion
- million = t$1,1
- billion = t$1,2
- trillion = t$1,3
- quadrillion = t$1,4
- quintillion = t$1,5
- sextillion = t$1,6
- septillion = t$1,7
- octillion = t$1,8
- nonillion = t$1,9
The long list of illion numbers
- Meillion - 10^0.00219726562
- Dillion - 10^0.00439453125
- Tillion - 10^0.0087890625
- Teillion - 10^0.017578125
- Pillion - 10^0.0234375
- Hxillion - 10^0.046875
- Hpillion - 10^0.09375
- Oillion - 10^0.1875
- Eillion - 10^0.375
- Dillion - 10^0.75
- Hillion - 10^1.5
- Killion - 10^3
- Million - 10^6
- Billion - 10^9
- Trillion - 10^12
- Quadrillion - 10^15
- Quintillion - 10^18
- Sextillion - 10^21
- Septillion - 10^24
- Octillion - 10^27
- Nonillion - 10^30
- Decillion - 10^33
- Undecillion - 10^36
- Duodecillion - 10^39
- Tredecillion - 10^42
- Quattuordecillion - 10^45
- Quindecillion - 10^48
- Sexdecillion - 10^51
- Septemdecillion - 10^54
- Octodecillion - 10^57
- Novemdecillion - 10^60
- Vigintillion - 10^63
- Trigintillion - 10^93
- Quadragintillion - 10^123
- Quinquagintillion - 10^153
- Sexagintillion - 10^183
- Septuagintillion - 10^…
SMB1-plex
One of the previous googolisms I invented to estimate how many one-screen-big levels possible there would be in Super Mario Bros. took almost everything into account... except the sprite limit. This blog post will be doing that.
The original Super Mario Bros. could only have 5 entities loaded at a time. The new expression is (83)^(13*16)*3*5*2^5*(13*16*36)^5 and I define SMB1-plex as (83)^(208)*(7488)^5*480 which is the most simplified form of the expression.
"Mini OCF - Pt. 1"
So, normal OCFs collapse down uncountables to return countables, and this "mini OCF" collapses countables to return finite numbers. Therefore, I guess it's more of a googological notation then ordinal notation or collapsing function. I have created 4 mini OCFs in the past, and this article will be about them.
- 1 OAN (Ordinal Array Notation)
- 2 NOBAN 1.0 (New Ordinal-Based Array Notation)
- 3 NOBAN 2.0
- 4 TMOAN (Third, Modified Array Notation)
OAN is a fairly weak notation, but it's a start. Here is a definition:
- \([\alpha] = \alpha\)
- \([\alpha, n] = \alpha n\)
- \([\alpha, \omega] = \alpha^2 + 1\)
- \([\alpha, \omega^n] = \alpha^{n+1} + 1\)
- \([\alpha, \omega^\omega] = \alpha^{2n + 1} + 1\)
You could go past to ordinals like \(\varepsilon_0\), and I wrote down som…
Super fast-growing hierarchy (powerful recursion-based function)
Created this random family of super fast-growing functions defined via extreme recursion on each other that I made a while ago. I don't know whether they are uncomputable or not, but they seem to have the fastest growth rate out of all my functions, excluding the hyper hierarchy. Don't confuse anything below with transfinite ordinals, OCFs, etc.
- \(\psi_1(n) = n^n\)
- \(\psi_{\alpha+1}(n) = \psi_\alpha^n(n)\)
- \(\phi_m(n) = \psi_{m^n}^{mn}(m+n)\)
- \(\varepsilon_1(n) = \psi_n(\phi_n(n)\)
- \(\varepsilon_{\alpha+1}(n) = \varepsilon_{\alpha}^{\varepsilon_\alpha^{\varepsilon_\alpha((\alpha + 1) \uparrow \uparrow n)}((\alpha+1)^n)}((\alpha+1)n)\)
- \(\Omega_0(n) = \psi_n(\varepsilon_n(n))\)
- \(\Omega_{\alpha+1}(n) = \Omega_\alpha^{\Omega_\alpha(n)}(n \uparrow \…