Flan number
Flan number 2
Flan numbers (Japanese: フラン数) are numbers coined by Japanese googologist 巨大数大好きbot. There are several versions of Flan numbers.
Episode[]
The numbers are named after Flandre Scarlet (Japanese: フランドール・スカーレット, nickname: フラン)[1], who is a famous character in Japanese game series 東方Project.
One of the most famous versions Flan number 4 version 3 (Japanese: フラン数第四形態改三) was coined on 03/22/2018.[2] Its predecessor Flan number 4 version 2 (Japanese: フラン数第四形態改二) is known to be equal to 6, and is the origin of the tradition in one of Japanese googology communities that \(6\) is a large number with the Japanese phrase "6は巨大数", partially as a sort of a joke.[3][4][5][6]
Perhaps this episode is the origin of the number ６ later coined by Japanese googologist Nayuta Ito.
Versions[]
The following is a table of informations of versions.[7][8]
| version name | approximation |
|---|---|
| フラン数第一形態 | \(10^{10^{10^{670767}}}\) |
| フラン数第二形態 | \(f_{\omega^{\omega^{\omega}}}^6(5)\) |
| フラン数第三形態 | \(f_{\varepsilon_0}^7(6)\) |
| フラン数第四形態 | ill-defined |
| フラン数第四形態改 | ill-defined |
| フラン数第四形態改二 | \(6\) |
| フラン数第四形態改三 | \(f_{\varepsilon_4^{\varepsilon_4^{\varepsilon_4}}}(5)\) |
| フラン数第五形態改二 | \(5\) |
| フラン数第五形態改三 | \(f_{\varepsilon_{\omega^{\omega^{\omega^{\omega+2}}}}}(5)\) |
| フラン数第六形態改二 | ill-defined |
| フラン数第六形態改二甲 | ill-defined |
| フラン数第七形態改二 | ill-defined |
| フラン数準第八形態改二 | ill-defined |
| フラン数最終形態・冬 | \(f_{\varepsilon_{\omega^{\omega^{\omega^{\omega}}}}}(5)\) |
| フラン数最終形態・終 | canceled |
| フラン数最終形態・了 | ill-defined |
| フラン数最終形態・焉 | ill-defined |
| フラン数最終形態・完 | ill-defined |
Here, \(f\) denotes the fast-growing hierarchy associated to Veblen hierarchy.
Japanese letters[]
The word "フラン" means "Flan", i.e. the nickname of Flandre Scarlet, and the letter "数" means "number". Therefore the combination "フラン数" means "Flan number". The letter "第" means "-th", and the letters "一", "二", "三", "四", "五", "六", "七", and "八" mean "1", "2", "3", "4", "5", "6", "7", and "8" respectively. Therefore for example, the combination "第三" means "third". The word "形態" means "form" or "version". The letter "改" means "revision", and hence the combination "改二" means "revision 2", i.e. the second revision. The letter "甲" means "first" in one of Japanese old counting systems. Therefore the combination "フラン数第六形態改二甲" means "The first version of the second revision of the sixth form of Flan number".
The word "形態" means "form" or "shape", and "最終" means "final". Therefore "フラン数最終形態" means "The final form of Flan number", although there are five forms of フラン数最終形態. The word "冬" for the first final form means the winter, but is just regarded as the right half side of the word "終". The word "終" for the second final form means "finished", and hence "フラン数最終形態・終" means "The final form of Flan number - the finale". The word "了" for the third final form means "completed", and hence "フラン数最終形態・了" means "The final form of Flan number - the denouement". The word "焉" for the fourth final form means "terminated", and hence "フラン数最終形態・焉" means "The final form of Flan number - the terminus". The word "完" for the last final form means "concluded", and hence "フラン数最終形態・完" means "The final form of Flan number - the end".
External links[]
- 西宮 七南-解説channel, ゆっくりと学ぶ巨大数論～フラン数第一形態～, YouTube. (An introduction video of フラン数第一形態)
- 西宮 七南-解説channel, ゆっくりと学ぶ巨大数論～フラン数第二形態～, YouTube. (An introduction video of フラン数第二形態)
- 猫山にゃん太, Flan Number 4th - フラン数第四形態 改二/改三, GitHub Page. （A javascript code to compute expansions of フラン数第四形態改二/改三）
Sources[]
- ↑ ピクシブ百科事典 - フランドール・スカーレット
- ↑ 巨大数大好きbot, Definition of Flan number 4 version 3, twitter.
- ↑ 叢武, 6は巨大数, twitter.
- ↑ 巨大数大好きbot, Definition of Flan number 4 version 2, twitter.
- ↑ rpakr, The statement that Flan number 4 version 2 coincides with 6, twitter.
- ↑ Hexirp, What is the origin of 6?, Japanese Googology Wiki user blog.
- ↑ FHLASR, 東方巨大数2エントリー一覧, Google spreadsheet.
- ↑ FHLASR, 第4回東方巨大数巨大数投稿一覧, Googleスプレッドシート.
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