White-aster notation is a notation for large numbers made by aster in a video on September 17, 2017[1][2].
This is an extension of Steinhaus-Moser Notation, which is one of the notations for large numbers.
It is extended by adding the concept of stars and levels in addition to the usual polygons.
Definition[]
First, we introduce the terminology to explain White-aster notation.
1.To simplify writing down the definitions, A string of integers greater than or equal to 3 or Ast is called a "figure type" as the only terminology used here, and a star is formally called "a Ast-gon".
2.For a figure of type p and integer n, a figure with <n> on the right shoulder of a regular p-gon is called "a p-gon of level n". For example, a regular triangle at level 4 is \(\triangle^{\langle 4 \rangle}\), and a star at level 5 is \(\textrm{☆}^{\langle 5 \rangle}\).
3.Let a be a figure or an integer greater than or equal to 3. A figure with an inside a p-gon of level n is denoted p[a,<n>] and called "a inside a regular p-gon of level n". For example, 3[5,<4>], which is 5 inside a regular 3-gon of level 4, is shown on the left in the figure below, 4[Ast[7,<6>],<5>], a 7 in a star of level 6 in a regular tetragon of level 5, is shown on the right below.
Based on this, the calculation of the White-aster notation is shown below.
Rule 1-1. If p = 3 and n=1, \[3[a,\langle 1 \rangle] = a^{a}\]
Rule 1-2. If p = Ast, \[\text{Ast}[a,\langle n \rangle] = a[a,\langle n \rangle]\]
Rule 2-1. If p = 3 and n > 1, \[3[a,\langle n \rangle] = \underbrace{\text{Ast}[\text{Ast}[\cdots[\text{Ast}}_{a}[a,\langle n-1 \rangle],\langle n-1 \rangle],\cdots],\langle n-1 \rangle],\langle n-1 \rangle]\]
Rule 2-2. If Rule 2-1 does not apply, \[p[a,\langle n \rangle] = \underbrace{p-1[p-1[\cdots[p-1}_{a}[a,\langle n \rangle],\langle n \rangle],\cdots],\langle n \rangle],\langle n \rangle]\]
Examples[]
5[2,<1>]
=4[4[2,<1>],<1>]
=4[3[3[2,<1>],<1>],<1>]
=4[3[2^2,<1>],<1>]
=4[3[4,<1>],<1>]
=4[44,<1>]
=4[256,<1>]
This value is equal to Mega.
4[3,<2>]
=3[3[3[3,<2>],<2>],<2>]
=3[3[Ast[Ast[Ast[3,<1>],<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[3[3,<1>],<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[33,<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[27,<1>],<1>],<2>],<2>]
=3[3[Ast[27[27,<1>],<1>],<2>],<2>]
…
Issues[]
Computation programs[]
- みずどら, 式神巨大数エントリー_編集中, Japanese Googology Wiki user blog. (Verified by Okkuu according to (2020-08-28)_式神巨大数の近況報告#11)
See also[]
By Aeton: Okojo numbers · N-growing hierarchy
By 新井 (Arai): Arai's psi function
By aster: White-aster notation · White-aster
By バシク (BashicuHyudora): Primitive sequence number · Pair sequence number · Bashicu matrix system 1/2/3/4 original idea
By ふぃっしゅ (Fish): Fish numbers (Fish number 1 · Fish number 2 · Fish number 3 · Fish number 4 · Fish number 5 · Fish number 6 · Fish number 7 · S map · SS map · s(n) map · m(n) map · m(m,n) map) · Bashicu matrix system 1/2/3/4 formalisation · TR function (I0 function)
By Gaoji: Weak Buchholz's function
By じぇいそん (Jason): Irrational arrow notation · δOCF · δφ · ε function
By 甘露東風 (Kanrokoti): KumaKuma ψ function
By koteitan: Bashicu matrix system 2.3
By mrna: 段階配列表記 · 降下段階配列表記 · 多変数段階配列表記 · SSAN · S-σ
By Naruyoko Naruyo: Y sequence formalisation · ω-Y sequence formalisation
By Nayuta Ito: N primitive · Flan numbers (Flan number 1 · Flan number 2 · Flan number 3 · Flan number 4 version 3 · Flan number 5 version 3) · Large Number Lying on the Boundary of the Rule of Touhou Large Number 4 · Googology Wiki can have an article with any gibberish if it's assigned to a number
By Okkuu: Extended Weak Buchholz's function
By p進大好きbot: Ordinal notation associated to Extended Weak Buchholz's function · Ordinal notation associated to Extended Buchholz's function · Naruyoko is the great · Large Number Garden Number
By たろう (Taro): Taro's multivariable Ackermann function
By ゆきと (Yukito): Hyper primitive sequence system · Y sequence original idea · YY sequence · Y function · ω-Y sequence original idea
By バシク (BashicuHyudora): Bashicu matrix system as a notation template
By じぇいそん (Jason): Shifting definition
By mrna: Side nesting
By Nayuta Ito and ゆきと (Yukito): Difference sequence system
By ふぃっしゅ (Fish): Ackermann function
By koteitan: Ackermann function · Beklemishev's worms · KumaKuma ψ function
By Mitsuki1729: Ackermann function · Graham's number · Conway's Tetratri · Fish number 1 · Fish number 2 · Laver table
By みずどら: White-aster notation
By Naruyoko Naruyo: p進大好きbot's Translation map for pair sequence system and Buchholz's ordinal notation · KumaKuma ψ function · Naruyoko is the great
By 猫山にゃん太 (Nekoyama Nyanta): Flan number 4 version 3 · Fish number 5 · Laver table
By Okkuu: Fish number 1 · Fish number 2 · Fish number 3 · Fish number 5 · Fish number 6
By rpakr: p進大好きbot's ordinal notation associated to Extended Weak Buchholz's function · Standardness decision algorithm for Taranovsky's ordinal notation
By ふぃっしゅ (Fish): Computing last 100000 digits of mega · Approximation method for FGH using Arrow notation · Translation map for primitive sequence system and Cantor normal form
By Kihara: Proof of an estimation of TREE sequence · Proof of the incomparability of Busy Beaver function and FGH associated to Kleene's \(\mathcal{O}\)
By koteitan: Translation map for primitive sequence system and Cantor normal form
By Naruyoko Naruyo: Translation map for Extended Weak Buchholz's function and Extended Buchholz's function
By Nayuta Ito: Comparison of Steinhaus-Moser Notation and Ampersand Notation
By Okkuu: Verification of みずどら's computation program of White-aster notation
By p進大好きbot: Proof of the termination of Hyper primitive sequence system · Proof of the termination of Pair sequence number · Proof of the termination of segements of TR function in the base theory under the assumption of the \(\Sigma_1\)-soundness and the pointwise well-definedness of \(\textrm{TR}(T,n)\) for the case where \(T\) is the formalisation of the base theory
By 小林銅蟲 (Kobayashi Doom): Sushi Kokuu Hen
By koteitan: Dancing video of a Gijinka of Fukashigi · Dancing video of a Gijinka of 久界 · Storyteller's theotre video reading Large Number Garden Number aloud
See also: Template:Googology in Asia
Sources[]
- ↑ https://www.nicovideo.jp/user/67584421
- ↑ https://www.nicovideo.jp/watch/sm31940678 from 11 min 40 sec