SSAN

SSAN is a notation introduced by a Japanese Googology Wiki user mrna,The user page of mrna in Japanese Googology Wiki. 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 摩多羅隠岐奈摩多羅隠岐奈 in pixiv dictionary. in Japanese famous video game series 東方Project, and the name of the third number comes from nicknames of characters 爾子田里乃爾子田里乃 in pixiv dictionary. and 丁礼田舞丁礼田舞 in pixiv dictionary. 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.mrna, 七星の剣数. 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.mrna, 絶対秘神の七星剣数.mrna, 二童子達のバックナンバーズ. 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 ==
* side nesting
Category:Numbers
Category:Functions
Category:Side nesting
Category:Googology in Asia
Category:Incomplete
Category:Higher computable level
Category:Unformalised