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Clyde1000^1000 Clyde1000^1000 54 minutes ago
0

Extended Arrow Notation

This is a fixed version of my new notation and there will be analysis on it.

The notation, as I called, "extended arrow notation" is a bit silly considering that there are no arrows in the notation...

Lets define it!

a, b and c are natural numbers.

@ represents inactive "blocks" or nothing.

A1 and A2 stands for different arrays or nuffin.

stands for an array with only ones.

Any other letter stands for a integer number larger than 1.

NOTE: THIS ONLY WILL COVER ARRAY NOTATION.

a@1=a

a@[A1,]b=a@[A1]b

a[1]b=a^b

a@[1]b=a@a@[1](b-1)

a@[c+1,A1]b=a@[c,A1][c,A1][c,A1]... b times... [c,A1][c,A1][c,A1]b

a@[A1,1,k,A2]b=a@[A1,a@[A1,1,k,A2](b-1),k-1,A2]a

Time to analyze it!

a[1]b has 2 in FGH growth rate.

a[2]b has a ω in growth rate.

a[3]b has a ω^2 growth rate and so o…

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PersonWhoDontKnowBasic PersonWhoDontKnowBasic 19 hours ago
2

No Subject

Base-2 Function: (Binary Function)

Bit(0) = 0

Bit(1) = 1

Bit(2) = 10

Bit(3) = 11

Bit(4) = 100

Bit(5) = 101

Bit(6) = 110

Bit(7) = 111

Bit(8) = 1,000

Bit(9) = 1,001

Bit(10) = 1,010

Trinary Function: Not to be confused with Trinary Base-3

Trit(n) = Bit(Bit(Bit(...Bit(Bit(n))))... (n's Bit)

Trit(0) = 0

Trit(1) = 1

Trit(2) = 1,010

Trit(3) = 1,111,110,011

Trit(4) = 1,010,110,101,111,001,011,010,001,101,011,011,001,100,110,110,011,001,100,101,110,100,100

Trit(5) = 1.001100101... × 10^219

Trit(6) = 1.011010110... × 10^727

Trit(7) = 1.000010100... × 10^2,415

Trit(8) = 1.101101000... × 10^12,049

Trit(9) = 1.101010000... × 10^40,023

Trit(10) = 1.010001010... × 10^132,951

Quadrinary Function:

Quadrit(n) = Trit(Trit(Trit(...Trit(Trit(n))))... (n's Trit)

Quadrit(0) = 0

Quadrit(1) …

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11sD Tile 11sD Tile 22 hours ago
0

Googolnovemicosiplex

The googolnovemicosiplex (also known as googolennaisokaplex or googolplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplexplex) is equal to E100#30 = EEEEEEEEEEEEEEEEEEEEEEEEEEEEEE100 in Hyper-E notation.

It is also equal to , or a 1 followed by a Googoloctoicosiplex

zeroes. It is 10^^30^100+1 ( exact ) digits long.


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Scorcher007 Scorcher007 22 hours ago
1

Strength of TON considering non-Gandy ordinals

In this blog I want to present a hypothesis about the strength of TON. Taranovsky's main hypothesis assumed that the strength of the TON was Z2+PD. However, new analysis of Hypcos shows that the 2nd system of the main notation is weaker than previously thought because the rich structure of non-Gandy ordinals was underestimated. However, perhaps this should not affect the full strength of the TON, only weakening the systems by n-1.

According to Hypcos analysis:

     
  • Ω0 = C(Ω1,0) - ε0 = PTO of PA
  •  
  • C(εΩ1+1,0) = C(C(Ω21),0) = BHO = PTO of KPω or Δ11-CA+BI
  •  
  • ... ≤ C(C(C(...Ωn×2...,0),0),0) n times - ordinals with order type of a well-ordering Δ10 subset (computable) of ω or recursive ordinals
  •  
  • Ω1 = C(Ω2,0) = ω1CK = 1st ordinal with order type of a well-ord…
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MultiSoul MultiSoul 22 hours ago
0

A Semi-Unoriginal Tier-4 -illion Number Extension

One day I was just finding ideas for random -illions when i had the idea to turn the hierarchy chain from All Dimensions Wiki into -illion numbers.

So what did i do? Self explanatory ig.


Anyway here’s the list:


Kalillion - 10^(3x10^(3x10^3000)+3)

Mejillion - 10^(3x10^(3x10^3000000)+3)

Gijillion - 10^(3x10^(3x10^3000000000)+3)

Astillion - 10^(3x10^(3x10^(3x10^12))+3)

Lunillion - 10^(3x10^(3x10^(3x10^15))+3)

Fermillion - 10^(3x10^(3x10^(3x10^18))+3)

Jovillion - 10^(3x10^(3x10^(3x10^21))+3)

Solillion - 10^(3x10^(3x10^(3x10^24))+3)

Betillion - 10^(3x10^(3x10^(3x10^27))+3)

Glocillion - 10^(3x10^(3x10^(3x10^30))+3)

Gaxillion - 10^(3x10^(3x10^(3x10^33))+3)

Supillion - 10^(3x10^(3x10^(3x10^36))+3)

Versillion - 10^(3x10^(3x10^(3x10^39))+3)

Multillion - 10^(3x10^(3…



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WhoDoesntKnowBasic WhoDoesntKnowBasic 1 day ago
0

test

test


How do i delete it now?

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OmicsYT OmicsYT 1 day ago
1

Someone tell me please.

'

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Bruhify Army Bruhify Army 1 day ago
0

Holer's Number

Holer's Number is a huge number built on many fast-growing functions defined by Holersh.
There are two Holer's Number: the Small Holer's Number (𝔥) and the Large Holer's Number (ℌ).


The Basic Holer Function is defined as folows:


(WIP)

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Dhani irwanto Dhani irwanto 1 day ago
1

Isra miraj and the time of 50

This article was copied from a powerpoint created by Fahmi Basya, one of the lecturers at the Tarbiyah Faculty of Islamic State University Syarif Hidayatullah, everything in this article was not created by me, only translated into English, I got the presentation from the slideplayer website

This is not officially sourced from a real religion, just people who want to play with religion, but the principles here are not found in religious literature

There are several series of presentations in this article called flying books, I marked them in the form of headings in my blog post, Later I will provide the most complete sources for all presentations

I DID NOT MAKE THIS PRESENTATION

For those who feel offended by matters of religion and belief, plea…

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Xrjxj Xrjxj 2 days ago
1

X ordinal


1 separator "ω^2"

X=ω

Χ/1=ω+1

Χ/2=ω+2

X/X=ω*2

X/X/1=ω*2+1

X/X/X=ω*3

2 dividers "ε0"

X//1=X/X/…=ω^2

(X//1)/1=ω^2+1

(X//1)/2=ω^2+2

(X//1)/X=ω^2+ω

(X//1)/(X//1)=ω^2*2

(X//1)/(X//1)/(X//1)=ω^2*3

X//2=ω^3

(X//2)/(X//2)=ω^3*2

X//3=ω^4

X//X=ω^ω

X//X/1=ω^ω+1

X//X/X=ω^ω*2

X//X//1=ω^ω^2

X//X//X=ω^ω^ω

X//X//X//X=ω^ω^ω^ω

3 dividers "ζ0"

X///1=ε0

(X///1)/1=ε0+1

(X///1)/(X///1)=ε0*2

(X///1)/(X///1)/(X///1)=ε0*3

(X///1)//1=ε0*ω

((X///1)//1)/(X///1)=ε0*ω+1

((X///1)//1)/((X///1)//1)=ε0*ω*2

(X///1)//2=ε0*ω^2

(X///1)//3=ε0*ω^3

(X///1)//X=ε0*ω^ω

(X///1)//(X//X)=ε0*ω^ω^ω

(X///1)//(X//X//X)=ε0*ω^ω^ω^ω

(X///1)//(X///1)=ε0^2

(X///1)//(X///1)/1=ε0^2*ω

(X///1)//(X///1)/2=ε0^2*ω^2

(X///1)//(X///1)/(X///1)=ε0^3

(X///1)//(X///1)/(X///1)/(X///1)=ε0^4

(X///1)//(X///1)//1=ε0^ω

(X///1)//(X///1)//2=ε0^ω^2

(X///1)…


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Polymations Polymations 3 days ago
0

φ(ω,0) in ES5

EDIT: THIS IS ABSOLUTELY NOT ES5, it just has more ES5 than ES6

lprss([0,n],n) is about \(f_{\varphi_\omega(0)}(n)\) in the fast growing hierarchy.

493 characters, entirely compatible in the ES5 Enviroment, meaning you are always able to run it on any javascript console!


\(()[n]=n+1\)

\((a_1,a_2,a_3,...a_{k-2},a_{k-1},0)[n]=(a_1,a_2,a_3,...a_{k-2},a_{k-1})^n[n]\)

\((a_1,a_2,a_3,...a_{k-2},a_{k-1},a_{k})[n]=\text{expand}(a_1,a_2,a_3,...a_{k-2},a_{k-1},a_{k})[n]\)

\(m=a[\text{len}(a)], r = \min\{l\in a|l< m\}, \delta=m-r-1\)

\(G=(a_1,a_2,a_3,\ldots,a_{r-2},a_{r-1}),B = (a_r,a_{r+1},a_{r+2},\ldots,a_{k-2},a_{k-1})\)

\(\text{expand}(a,p)=G\cup \bigcup_{t=0,t< p}B+t\delta\) where \(A+b\) means all of \(A\)'s entries added by \(b\).


This is an implementat…



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Googology guy Googology guy 3 days ago
0

Creating my YouTube Channel

Hey guys,I have created my YouTube Channel,Im still going to upload videos soon,But im already preparing it,Anyways,If you want to find it,Here is the link:

https://www.youtube.com/@ValentinoScientist

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Xrjxj Xrjxj 3 days ago
0

The whole "k" massif in 1 post


part l

k{1}=10

k{2}=10^10

k{3}=10^10^10

k{1,2}=k{10}


k{1,,2,2}=k{1(2*)2,,1,2}

k{1,,1,3}=k{1,,10,2}

k{1,,1,1,2}=k{1,,1,10}

k{1,,1(2)2}=k{1,,1,1,…,1,2}

k{1,,1,,2}=k{1,,1(2*)2}

k{2,,1,,2}=k{1,,1(2**)2}

k{1,,2,,2}=k{1(2*)2,,1,,2}

k{1,,1,,3}=k{1,,1(2*)2,,2}

k{1,,1,,1,,2}=k{1,,1,,10}

part Vl (α version)

k{1(2,,)2}=k{1,,1,,…10}

k{1(2,,)3}=k{1,,1,,…,,1,,2(2,,)2}

k{1(3,,)2}=k{1(2,,)1(2,,)…10}

k{1(4,,)2}=k{1(3,,)1(3,,)…10}

k{1(1,2,,)2}

k{1(1(1,2,,)2,,)2}

k{1(2*,,)2}=k{1(1(…(1(1(1,2,,)2,,)2,,)…)2,,)2}

k{1(2**,,)2}=k{1(1(…(1(1(1,2*,,)2*,,)2*,,)…)2*,,)2}

k{1(2***,,)2}=k{1(1(…(1(1(1,2**,,)2**,,)2**,,)…)2**,,)2}

k{1,,,2}=k{1(2*,,)2}

k{2,,,2}=k{1(2**,,)2}

k{1,,,3}=k{1(2*,,)2,,,2}

k{1,,,1,,,2}=k{1,,,1(2*,,)2}

k{1(2,,,)2}=k{1,,,1,,,…10}

k{1(1,2,,,)2}

k{1(1(1,2,,,)2,,,)2}

k{1,,,,2}=k{1(…



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Polymations Polymations 3 days ago
0

HNS extension 1

(I analyzed it in my head and the limit ordinal is only \(\varepsilon_1\))

A Hyper N-Ary Double-Sequence is in the form \(\langle A_{1}\rangle\langle A_{2}\rangle\langle A_{3}\rangle\ldots\langle A_{k-2}\rangle\langle A_{k-1}\rangle\langle A_{k}\rangle[n]\)

If the sequence is \(\langle 0 \rangle\), then return n+1.

Otherwise, if it ends with \(\langle 0 \rangle\), then \(\langle A_{1}\rangle\langle A_{2}\rangle\langle A_{3}\rangle\ldots\langle A_{k-2}\rangle\langle A_{k-1}\rangle\langle A_{k}\rangle[n] = (\langle A_{1}\rangle\langle A_{2}\rangle\langle A_{3}\rangle\ldots\langle A_{k-2}\rangle\langle A_{k-1}\rangle)^n[n]\), where \(f^a(b)\) represents function iteration.

Otherwise, if the last sequence ends with \(\langle\ldots0\rangle\), then…

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Natsugoh Natsugoh 4 days ago
0

Solving the functional equation a◦f = g◦a for f and for g

Abstract

The functional equation \(a \circ f = g \circ a\) with \(f: X \to X\) and \(g: Y \to Y\) is an Abel equation when \(f = s\), the successor function. That is generalization of the iterate of \(g\).

We provide an expression for \(g\) in terms of \(a\) and \(f\). That is an "unitetate" of \(g\) when \(f = s\).


  • 1 Main text
    • 1.1 Lemma 1.1.
    • 1.2 Definition 1.2.
    • 1.3 Lemmma 1.3.
    • 1.4 Lemma 1.4.
    • 1.5 Proposition 1.5.
    • 1.6 Corollary 1.6.
    • 1.7 Example 1.7.


PDF: https://drive.google.com/file/d/1D1QFIPzsM0I8kiK8m9SLL4cFzhPlQQV6/view?usp=sharing

Old PDF: https://drive.google.com/file/d/1dgi1s4isEMUAmoQQcA22oszKpPGmc-F4/view?usp=sharing

\[ \newcommand{\U}[1]{\mathcal{U}_{#1}} \]




From here, let \(\sim_f\) denotes the equivalence kernel of a function \(f\); \(a \sim_f b :\if…






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Polymations Polymations 5 days ago
1

N-ary System Extension Using Broken Integers

Broken integers are numbers such that the previous number minus it is less than -1.

for example, the broken integer in [0,1,2,3,4,2,3,5,6,7] is 5, since 3-5 < -1.

Revised expansion definition:

If the last number of the sequence is 0, stop this process, otherwise:

Let p be the last number of a sequence

If there exists p-1 in the sequence, "select" everything from the last number that is p-1, delete p from the sequence, and duplicate the sequence p times.

If there doesn't exist p-1 in the sequence, and p is less than or equal to the number before it, duplicate the sequence with each duplicate's number being increased by p-1. E.g. [0,2,2] = [0,2,1,3,2,4,3,5,...]

If there doesn't exist p-1 is the sequence, and p is greater than the number before it (m…

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X0dewG X0dewG 5 days ago
0

Inferniation


  1. a|b=[a][a][a][a][a][a][a][a]... with b copies of [a]-s.
  2. a||b=a|a|a|a|a|a|a... with b copies of a-s.
  3. a|||b=a||a||a||a||a||a... with b copies of a-s.
  4. a||b=a|2b
  5. a|||||...b with c copies of |-s.
  6. So a|cb=a|c-1a|c-1a|c-1a|c-1a... with b copies of a-s.
  7. a||cb=a|da|da|da... with b copies of a-s, d=a|cb.
  8. a|||cb=a||da||da||da||da... with b copies of a-s, d=a||cb.
  9. a||||cb=a|||da|||da|||da|||da... with b copies of a-s, d=a|||cb.
  10. a||||cb=a||||da||||da||||da||||da... with b copies of a-s, d=a||||cb.
  11. a|ecb=a|e-1da|e-1da|e-1da... with b copies of a-s, d=a|e-1cb.
  12. So: a|2cb=a||cb, a|3cb=a|||cb, a||||cb=a|4cb
  13. a||ecb=a|eca|eca|eca|eca|eca|eca|eca... with b copies of a-s.
  14. a|||ecb=a||eca||eca||eca||eca||eca||eca||eca... with b copies of a-s.
  15. a||||ecb=a|||eca|||eca…


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Tamatak sockpuppet Tamatak sockpuppet 5 days ago
2

what is the largest number that can be calculated at scratch.mit.edu

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Xrjxj Xrjxj 6 days ago
2

strong extension of the Veblen function


before ψ(Ω2)

φ(1#ω)=ψ(Ω^ω)

φ(1#φ(1#1))=ψ(Ω^ψ(Ω))

φ(1#φ(1#φ(1#1)))=ψ(Ω^ψ(Ω^ψ(Ω)))

φ(1#1,0)=ψ(Ω^Ω)

φ(1#1,1)=ψ(Ω^Ω+1)

φ(1#1,2)=ψ(Ω^Ω+2)

φ(1#1,φ(1#1,0))=ψ(Ω^Ω+ψ(Ω^Ω))

φ(1#2,0)=ψ(Ω^Ω*2)

φ(1#3,0)=ψ(Ω^Ω*3)

φ(1#φ(1#1,0),0)=ψ(Ω^Ω*ψ(Ω^Ω))

φ(1#1,0,0)=ψ(Ω^Ω^2)

φ(1#1,0,0,0)=ψ(Ω^Ω^3)

φ(2#0)=φ(1#0)=φ(0)

φ(2#1)=φ(1#1,0)

φ(2#2)=φ(1#1,0,0)

φ(2#ω)=ψ(Ω^Ω^ω)

φ(2#φ(2#1))=ψ(Ω^Ω^ψ(Ω^Ω))

φ(2#1,0)=ψ(Ω^Ω^Ω)

φ(2#1,1)=ψ(Ω^Ω^Ω+1)

φ(2#2,0)=ψ(Ω^Ω^Ω*2)

φ(2#1,0,0)=ψ(Ω^Ω^Ω^2)

φ(2#1,0,0,0)=ψ(Ω^Ω^Ω^3)

φ(3#ω)=ψ(Ω^Ω^Ω^ω)

φ(3#1,0)=ψ(Ω^Ω^Ω^Ω)

φ(4#1,0)=ψ(Ω^Ω^Ω^Ω^Ω)

before ψ(Ω2^ω)

φ(ω#0)=ψ(Ω2)

φ(ω#1)=ψ(Ω2+1)

φ(ω#2)=ψ(Ω2+2)

φ(ω#1,0)=ψ(Ω2+Ω)

φ(ω#1,0,0)=ψ(Ω2+Ω^2)

φ(ω+1#ω)=ψ(Ω2+Ω^ω)

φ(ω+1#1,0)=ψ(Ω2+Ω^Ω)

φ(ω+2#1,0)=ψ(Ω2+Ω^Ω^Ω)

φ(ω*2#0)=ψ(Ω2*2)

φ(ω*2#1,0)=ψ(Ω2*2+Ω)

φ(ω*2+1#1,0)=ψ(Ω2*2+Ω^Ω)

φ(ω*3#0)=ψ(Ω2*3)

φ(ω*4#0)=ψ(Ω2*4)

φ(ω…


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Tamatak sockpuppet Tamatak sockpuppet 6 days ago
0

how big is the sam number actually? PART II

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TrialPurpleCube TrialPurpleCube 6 days ago
0

BO without ordinal-like objects

This is a function which (at least when written down) does not use any ordinal-like objects. That is, it is written entirely using numbers. However, the definition does use ordinals. Assume FSes are the ones for ExBuchholz. \begin{eqnarray*} t(k,n) &=& \max\{α \mid g_α(n) = k\} \\ λ(k,n) &=& \begin{cases}n+1 & [k = 0] \\ λ(g_{t(k,n)}(n+1)-1,n+1) & [t(k,n) \in \text{Suc}] \\ λ(g_{t(k,n)[n]}(n+1),n+1) & [t(k,n) \in \text{Lim}]\end{cases} \\ N_0 &=& 2 \\ N_{n+1} = λ(N_n,2) \\ \end{eqnarray*} \(N_n\) grows at the level of Buchholz's ordinal.

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Polymations Polymations 7 days ago
1

Simplified JS Code for Hyper N-ary System

hns([0,1,2,3,4,5,6,7,8,9,...],n) \(\leq f_{\varepsilon_0}(n)\)

362 characters, originally used to be 1021 characters

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Kanrokoti Kanrokoti 7 days ago
0

Introduction of post-EBO

Japanese version


  • 1 Overview
  • 2 But why 3-var ?
  • 3 Their difference in expansion
  • 4 Correspondences to cardinals
  • 5 Cofinality of terms


If you view this from a smartphone, enabling desktop mode of your browser will allows it to display formulas. Also, in case you find ads are annoying, you can turn them off from personal setting, which is available after logging in.

I introduce the world of post-EBO. In this blog post, I use OFP 3-var ψ and 3-var ψ as post-EBO notations. OFP 3-var ψ goes beyond EBO by extending the ON of EBOCF to 3-var simply. 3-var ψ goes beyond EBO by extending the ON of EBOCF to 3-var naturally.

Therefore, I assume the reader has sufficient understanding to the ON of EBOCF hereafter.



First of all, why do both notation form 3-var ? - That'…





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Msiajoe74 Msiajoe74 7 days ago
1

SVO, LVO and Beyond

Veblen Notation that builds a string of ordinals are simple and elegant. On this blog, I would like to explore the limit it can go, in layman's language.


  • 1 Basic Concept
  • 2 Small Veblen Ordinal (SVO) and Large Veblen Ordinal (LVO)
  • 3 Beyond LVO
  • 4 Examples
  • 5 Weird Notes


First, let's start with φ(α,0), where α denotes any ordinal. Then we have

φ(α) = ωα

and φ(1,0) = ε0 = ωωωωω = φ(φ(φ ... (φ(φ(0))) ... )) (with ω copies of φ's)

and φ(1,α) = εα

Next we have

and φ(2,0) = ζ0 = εεεε0 = φ(1,φ(1,φ( ... 1,φ(1,φ(1,0)) ... ))) (with ω copies of φ's)

and φ(2,α) = ζα

and so on.


We define φ(α@ω) = φ(α,0,0, ... ,0,0) (with ω copies of 0's), so

SVO = φ(1@ω)

= {φ(1), φ(1,0), φ(1,0,0), φ(1,0,0,0), ...}

= {ω, ε0 , Γ0 , Ackermann ordinal, ...}

Next we have

LVO = φ(1@@ω)

= φ(1@φ(1@φ( ...…




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OllieZ123 OllieZ123 9 days ago
0

RO

Heads-Tri-1-primol Clover mite-bunch Octal-pipsqueak

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Xrjxj Xrjxj 9 days ago
1

k array part of Vll and Vlll


part Vll

k{1(2*(1))2}=k{1(2*)2}

k{1(2*(2))2}=k{1(2**)2}

k{1(2*(3))2}=k{1(2***)2}

k{1(2*(1,2))2}

k{1(2*(2(2)2))2}

k{1(2*(2(2*(1,2))2))2}

k{1(2*(2(2*(1(2*(1,2))2))2))2}

k{1(2*(1*))2}=k{1(2*(1))2}

k{1(2*(2(1*))2}=k{1(2*(2))2}

k{1(2*(1,2(1*))2}=k{1(2*(1,2))2}

k{1(2*(1(2*(1,2(1*))2(1*))2}=k{1(2*(1(2*(1,2))2))2}

k{1(2*(2*))2}=k{1(2*(…(1(2*(1,2(1*))2*(1*))2(1*))…))2(1*))2}

k{1(2*(3*))2}=k{1(2*(…(1(2*(1,2(2*))2*(2*))2(2*))…))2(2*))2}

k{1(2*(1,2*))2}

k{1(2*(1(2*(1,2*))2*))2}

k{1(2*(1(2*(1(2*(1,2*))2*))2*))2}

k{1(2*(2**))2}=k{1(2*(…(1(2*(1,2*))2*))2*))…))2*))2}

k{1(2*(2***))2}=k{1(2*(…(1(2*(1,2**))2**))2**))…))2**))2}

k{1(2*(2****))2}=k{1(2*(…(1(2*(1,2***))2***))2***))…))2***))2}

k{1(2*(2*(1,2)))2}=k{1(2*(2**…**))2}

k{1(2*(2*(2*(1,2))))2}

k{1(2*(2*(2*(2*(1,2)))))2}


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Nēêrżžź Nēêrżžź 9 days ago
0

Repetition notation

(1)[0]=0

(2)[0]=0

(n)[0]=0

(n)[h]=h

(N)[]=(n)[n]

(n)[10]=(n)[n+1]

(n)[20]=(n)[10][10]

(n)[30]=(n)[20][20][20]

(n)[h+10]=(...(n)...)[h0]...h+1...[h0]

(n)[11]=(n)[n0]

(n)[21]=(n)[n+10]

(n)[12]=(n)[n1]

etc...

(n)[]=(n)[nn]

(n)[]=(n)[nn]

etc...

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OllieZ123 OllieZ123 10 days ago
0

Imnino

List of googolisms/Class 2

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Nēêrżžź Nēêrżžź 10 days ago
1

X function

X(1)=10

x(n+1)=x(n)^=x(n)^n^^n

x(n+1,h+1)=x(n,h){h-1}(n{h}n)

x(n,1)=x(n)

x(1,n)=10^n

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OllieZ123 OllieZ123 11 days ago
0

1018-101001100101010101011010100110101010101010100100000

Foohol Sesexagintacentillion Pampena's Prime Septensexagintacentillion Googoocix 10^512 Astrigol Septuagintacentillion some random plex Googocci Googoocxij Quinseptuagintacentillion Googocciv Maximusquadrillion Pentlastillion Femtillion Googolquintigong Decans Dupixul

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Polymations Polymations 12 days ago
0

Ultra N-ary Sequence System

The following definition is an extension of the Hyper N-ary Sequence System, whose growth rate is \(\varepsilon_0\).

Take an array of natural numbers whose first number is 1, and assign an index to it. The full format should look like [index]. Let l(A) represent all but the last element of A. Now do the following:

If the array you took is [1], return the index+1.

If the array isn't [1], but ends with 1, then return ^i[i], where f^x represents function iteration. For example, [4] = [[4]] and [4] = [[4]]

Otherwise, do the following expansion process until it ends with a 1:

Let p be the 2nd entry in a sequence, and v be the first line of the number p before another number that isn't p. If p=3:
If there are only 2 numbers in the sequence, then is t…
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OllieZ123 OllieZ123 12 days ago
0

M.O.T

3


9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 Fznine Ternary-guppychunk Ternary-guppy 3^21

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Polymations Polymations 12 days ago
1

Epsilon-0 in javascript

This is a new system I call the Hyper N-ary Sequence System. Valid arrays in this system are called Hyper N-ary Sequences.

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X0dewG X0dewG 13 days ago
1

The ascending factorial notation

I can explain it more in the comments if you do not understand.


  • 1 Base Pattern
  • 2 The extended pattern
  • 3 Fully Extended
  • 4 Pure extension
  • 5 Absolute extension
  • 6 Inferniation


  1. a[!]b=a+(a+1)+(a+2)+(a+3)...a+(b-1)+(a+b)=a[![1]b
  2. a[![2]b=a×(a+1)×(a+2)×(a+3)...a+(b-1)×(a+b)
  3. a[![3]b=a↑(a+1)↑(a+2)↑(a+3)...a+(b-1)↑(a+b)
  4. a[![4]b=a↑b(a+1)↑b(a+2)↑b(a+3)...a+(b-1)↑b(a+b)
  5. a[![5]b=a{b}b(a+1){b}b(a+2){b}b(a+3)...a+(b-1){b}b(a+b)
  6. a[![6]b=a{b}a[![5]b(a+1){b}a[![5]ba+2){b}a[![5]ba+3)...a+(b-1){b}a[![5]b(a+b)
  7. a[![6]b=a{b}a[![6]b(a+1){b}a[![6]ba+2){b}a[![6]ba+3)...a+(b-1){b}a[![6]b(a+b)
  8. a[![b]c=a{c}a[![b-1]b(a+1){c}a[![b-1]ba+2){c}a[![6]ba+3)...a+(c-1){c}a[![b-1]b(a+c) if b>6
  9. a[![b[d]c=a{c}a[![b-1]b(a+1){c}a[![b-1]ba+2){c}a[![6]ba+3)...a+(c-1){c}a[![b-1]b(a+c){c}a[![b-1]b(a+1){c}a[![…



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Warlter545 Warlter545 13 days ago
1

Warlter's Square Brackets Notation

Warlter's Square Brackets Notation is a notation defined by Warlter545.


Define recursively as below

  1. \([][n]=n\)
  2. \([a+1,_1X][n]=[a,_1X][f(n)]\)
  3. \([X,_10,_1b+1,_1X][n]=[X,_1n,_1b,_1X][n]\)
  4. \([X,_m0][n]=[X,_m][n]\)
  5. \([X,_1c,_{d+1},X][n]=[X,_1\underbrace{c,_dc,_d…c,_d}_n,X][n]\)

If 1 is not suitable, check 2, if 2 is not suitable, check 3, if 3 is not suitable, check 4, if 4 is not suitable, check 5

Check 3 and 5 from the left, and calculate only the first place that satisfies the rule.

Also, \(X\) are numbers greater than or equal to 0 and greater than or equal to 0.

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OllieZ123 OllieZ123 14 days ago
0

10729-1010100

Duoquadragintaducentillion Sesquinquagintaducentillion Ogolchime Novenonagintaducentillion Trecentillion Octal-googolchime Astrapengol 10^999 Phichime Eulerchime Pichime Googolchime Octyillion Googgool 10^1200 Quadringentillion Hexadecimal-Goomol Quingentillion Ecetonding Duodeciquingentillion 10^1600 Sescentillion

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Nēêrżžź Nēêrżžź 14 days ago
0

Test

How do i delete this help please

well i guess this is a test so...



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Xrjxj Xrjxj 15 days ago
2

Why are you ignoring my blog posts?

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Barrianic Barrianic 16 days ago
0

an OCF

Attempt No. 3 is at least my 4th or 5th attempt to making an ordinal collapsing function and is my 3rd attempt to making an OCF more powerful than Rathjen's Psi (hence the name Attempt No. 3)


Let L be equal to c in the base booster system at nlevels=2

\(\{L\}\cup(L\cap(enum[\{\alpha|\alpha\in S\land\forall\beta\in\alpha\exists\gamma\in\alpha\cap S\land\beta\in\gamma\}](\delta)\bigcup_{\epsilon\in\delta}St_{0} ^{\epsilon}(S)))\subseteq St_{0} ^{\delta}(S)\)

\(\beta\not\in L\land\beta,\gamma\in St_{\alpha} ^{\delta}(S)\cup sup(St_{\alpha} ^{\delta}(S)\cap L)\rightarrow\beta+\gamma,\omega^{L+\gamma}\in St_{\alpha} ^{\delta}(S)\)

\(\epsilon\in S \land(\forall\gamma\in\delta(\forall(\beta\in\alpha\cap(St_{\alpha} ^{\gamma}(S)\cup\epsilon)\forall(T\…


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OllieZ123 OllieZ123 16 days ago
0

How y???e is corrected it’s not your but is you’re

Meet yourself in 105 degrees Celsius

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Nēêrżžź Nēêrżžź 16 days ago
0

Hash notation

A#b=a^^...a... a^^...a... b layers ...a...^^a ...a...^^a

a##1=a#a#a...a...a

a##b=(a##(b-1))##(b-1)

a###1=a##a##...a...a

a###b=(A###(b-1))###(b-1)

etc...

a(#^c)b=a###...c...###b

a#-[2]b=a## ...a... ##... b layers ...## ...##a

a##-[2]b=a##-[2]a#-[2]...b...a

etc...

a#-[3]b=a##...a##...b layers... ##a-[2]...##-[2]a

a#-[4]b=a##...a##...b layers... ##a-[3]...##-[3]a

etc...

a#-[#]b=a#-[a#-[...b layers...[a]...b layers..]a]a

a##-[#]1=a#-[#]...b...a

a##-[#]b=(A##-[#](b-1))##-[#](b-1)

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GamesFan2000 GamesFan2000 16 days ago
0

A New Array Notation Inspired By Lawrence Hollom

Hey, I've come out of hibernation to do something googology-related! This post has a link to a document featuring the first part of my new array notation, heavily inspired by Lawrence Hollom's Hyperfactorial Array Notation, or the linear part of it at least. https://docs.google.com/document/d/1AUVnf4EnwGSAWAB5cKYiB2d3QrChL1scjlEqVouwIwM/edit?usp=sharing

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OllieZ123 OllieZ123 17 days ago
0

Illions

1 10 100 Thousand Myriad Lakh Million Crore 100000000 Billion 10^10 10^11 10^12 10^13 10^14 Quadrillion 10^16 10^17 10^18 Guppychunk Guppy Sextillion 10^22 10^23 10^24 10^25 10^26 Octillion 10^28 10^29 10^30 10^31 10^32 Decillion 10^34 Goby Undecillion 10^37 10^38 Duodecillion 10^40 10^41 10^42 10^43 10^44 Quattuordecillion 10^46 10^47 Quindecillion 10^49 Lcillion 10^51 10^52 Tallakshana 10^54 10^55 Asougi Octodecillion 10^58 10^59 10^60 10^61 10^62 Vigintillion 10^64 10^65 Unvigintillion 10^67 Muryoutaisuu Duovigintillion Ogolspeck 10^71 Tresvigintillion 10^73 10^74 Quattuorvigintillion 10^76 10^77 Quinvigintillion Ogolchunk Ogol

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OllieZ123 OllieZ123 17 days ago
0

Better

1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1014 1024 1050

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OllieZ123 OllieZ123 17 days ago
1

The gianting number ultra forever all multiversal extended part 1

20 21 22 23 23.6666666/gaz 24 25 27 30 32 36 40 phiplex 49 50 55 60 61/gagthree 64 70 80 81 85 90 100! 110 111 120 121 123 125 128 130 140 144 150 160 162 169 170 180 190 196 200 210 216 220 222 223 225 230 240 243 250 255 256 260 270 280 289 290 299 300 310 320 321 324 325 330 333 340 341 350 360 361 370 378 380 390 399 400 405 410 420 430 435 440 441 450 456 460 470 480 484 486 490 496 499 500! 510 520 eplex 529 543 550 567 599 600 616 625 648 666 700 753 777 800 847 894 900 909 990 999 999.9999999999999999999999 1,000! 1,001 1,024 Lily Gartreys Long thousand Unexian Maha Piplex Great gross Hardy-Ramanujan Number Eyelash mite-chunk 2048 Ternary-pipsqueak Great Baker's gross Planus Heads-Pentprimol Erbe Poulter's great gross 3000 Garking…

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Xrjxj Xrjxj 17 days ago
0

new version of the i array

A spontaneous idea occurred to me how this array can be made more beautiful and concise.

The first 2 parts are the same as before

The estimated growth rates: ε_ω in FGH

part lll

i[n,,2]=i[n,n]

i[n,,3]=i[n,n,n]

i[n,,n]=i[n(2)n]

i[n,,n,2]=i[n(2)n(2)n]

i[n,,n,3]=i[n(2)n(2)n(2)n]

i[n,,n,n]=i[n(3)n]

i[n,,n,n,2]=i[n(3)n(3)n]

i[n,,n,n,n]=i[n(4)n]

i[n,,n(2)n]=i[n,,n,n,…n]

i[n,,n(2)n(2)n]=i[n,,n(2)n,n,…n]

i[n,,n(3)n]=i[n,,n(2)n(2)…n]

i[n,,n(4)n]=i[n,,n(3)n(3)…n]

i[n,,n,,1]=i[n,,n]

i[n,,n,,2]=i[n,,n,n]

i[n,,n,,3]=i[n,,n,n,n]

i[n,,n,,n]=i[n,,n(2)n]

i[n,,n,,n,n]=i[n,,n(3)n]

i[n,,n,,n,n,n]=i[n,,n(4)n]

i[n,,n,,n,,n]=i[n,,n,,n(2)n]

i[n,,n,,n,,n,,n]=i[n,,n,,n,,n(2)n]

i[n(2,,)n]=i[n,,n,,…n]

i[n(2,,)n,2]=i[n(2,,)i[n(2,,)n]]

i[n(2,,)n,,2]=i[n(2,,)n,n]

i[n(2,,)n,,3]=i[n(2,,)n,n,n]

i[n(2…

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Xrjxj Xrjxj 17 days ago
0

Analysis of the "i" array


I'm not sure that the analysis is correct, so you can point out errors if there are any

before ε0:

i[n]=n

i[n,n]≈f2(n)

i[n,n,n]≈f3(n)

i[n,n,n,n]=f4(n)

i[n(2)n]=fω(n)

i[n(2)n+1]=fω(n+1)

i[n(2)n,2]=fω(fω(n))

i[n(2)n,n]=fω+1(n)

i[n(2)n,n,n]=fω+2(n)

i[n(2)n(2)n]=ω*2

i[n(2)n(2)n,n]=ω*2+1

i[n(2)n(2)n(2)n]=ω*3

i[n(3)n]=ω^2

i[n(3)n,n]=ω^2+1

i[n(3)n(2)n]=ω^2+ω

i[n(3)n(2)n(2)n]=ω^2+ω*2

i[n(3)n(3)n]=ω^2*2

i[n(3)n(3)n(3)n]=ω^2*3

i[n(4)n]=ω^3

i[n(5)n]=ω^4

i[n,,n]=ω^ω

i[n,,n,n]=(ω^ω)+1

i[n,,n(2)n]=(ω^ω)+ω

i[n,,n(2)n(2)n]=(ω^ω)+ω*2

i[n,,n(3)n]=(ω^ω)+ω^2

i[n,,n,,n]=(ω^ω)*2

i[n,,n,,n,,n]=(ω^ω)*3

i[n(2,,)n]=ω^ω+1

i[n(3,,)n]=ω^ω+2

i[n(4,,)n]=ω^ω+3

i[n,,,n]=ω^ω*2

i[n(2,,,)n]=ω^ω*2+1

i[n,,,,n]=ω^ω*3

i[n,,,,,n]=ω^ω*4

i[n,,,…,,,n]=ω^ω^2

n(3)n#n=ω^ω^2

n(3)n,2#n=(ω^ω^2)*2

n(3)n,3#n=(ω^ω^2)*3

n(3)n,n#n=ω…


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Gongxiang01 Gongxiang01 17 days ago
0

good references

Project:Policy said all main namespace article need a external source. But how to find to a good source? Today we have find some website to let you find sources fast:

  • MathWorld is Eric Weisstein created a website. When find the CITE AS is a method to referencing.
  • arXiv is a free distribution service and an open-access archive for nearly 2.4 million scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. Materials on this site are not peer-reviewed by arXiv.(Website introduction) It's a good reference and have a large number of the references.
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Warlter545 Warlter545 17 days ago
1

Warlter’s Number Version 1

日本語のページはここから開けます。

Warlter’s Number Version 1 is a number that made by Warlter545.


  • 1 Definition
    • 1.1 W function
    • 1.2 WW function
    • 1.3 Warlter’s Number Version 1



W function is a function based on ordinal numbers that determines the function from natural number to natural number for ordinal numbers α and α'. It is defined as follows.

  • If \(\alpha\) is 0:
    • If \(\alpha’\) is 0: \(W_{0,0}(n)=n+1\)
    • If \(\alpha’\) is \(\alpha’’’+1\): \(W_{\alpha’’’+1,0}(n)=W_{\alpha’’’,n}^n(n)\)
    • If \(\alpha’\) is a limit ordinal and it's not 0: \(W_{\alpha’,0}(n)=W_{\alpha’[n],0}(n)\)
  • If \(\alpha\) is \(\alpha’’+1\): \(W_{\alpha’,\alpha’’+1}(n)=W_{\alpha’,\alpha’’}^n(n)\)
  • If \(\alpha\) is a limit ordinal and it's not 0: \(W_{\alpha’,\alpha}(n)=W_{\alpha’,\alpha[n]}(n)\)

About \(W^k_{\al…




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Goggologist Goggologist 18 days ago
1

Bowers seems inactive now :(

It has been exactly 4 years since Bowers updated something about googology on his site.

On the last leap day (Feb 29, 2020), Bowers added a new number - wun. Unfortunately, it is a salad number. Even worse, imagine eating wun slices of pizza!

And since then, Bowers switched to study polytope instead of googology :(

I really hope Bowers would return to googology and BEAF and oblivion numbers will be made well-defined by Bowers himself...

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