- Not to be confused with SAN.
SSAN is a notation introduced by a Japanese Googology Wiki user mrna,[1] and is the first notation which employs side nesting. It consists of infinite systems 0-SSAN, 1-SSAN, 2-SSAN, …, and ω-SSAN.
There are three large numbers defined by SSAN: 七星の剣数, 絶対秘神の七星剣数, and 二童子達のバックナンバーズ. The names of the first two numbers come from spell cards of a character 摩多羅隠岐奈[2] in Japanese famous video game series 東方Project, and the name of the third number comes from nicknames of characters 爾子田里乃[3] and 丁礼田舞[4] in the series.
Definition[]
Although the full system is currently ill-defined, 0-SSAN has been defined.
0-SSAN[]
The first system 0-SSAN has already been formalised, and was used to define a large number 七星の剣数 submitted to a Japanese googological event.[5] This system can be roughly given by interpreting pair sequences with respect to Bashicu matrix system version 2.3 into labeled brackets. In particular, the limit of 0-SSAN corresponds to \(\psi_0(\Omega_{\omega})\) with respect to Buchholz's function.
1-SSAN[]
The second system 1-SSAN was partially defined, and was used to define two large numbers 絶対秘神の七星剣数 and 二童子達のバックナンバーズ submitted to a Japanese googology event.[6][7] However, many errors were found in the original definition of 1-SSAN, and hence the two large numbers were rejected by the referees of the event. Although 1-SSAN is intended to go beyond \(\psi(\Omega_{K+1})\) with respect to an undefined ordinal collapsing function \(\psi\) and the least weakly compact cardinal \(K\), it has not been completely defined yet.
Higher SSANs[]
The latter systems such as 2-SSAN and ω-SSAN have not been formalised, either. According to Yukito, the limit of ω-SSAN is expected to go beyond the limit of SY sequence, which is Yukito's unformalised notation expected to go beyond the limit of Y sequence, which is expected to go beyond the limit of Bashicu matrix system version 2.3 under the assumption of the terminations of their formalisations.
Sources[]
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