Y function

Y function is a sort of functions introduced by a Japanese googologist Yukito, and is a function which employs side nesting.The user page of Yukito in the Japanese Googology Wiki.Yukito, Y関数, the Japanese Googology Wiki user blog.Yukito, 2019年11月18日版0-Y関数+1-Y関数, Google Document.
== Versions ==
It has at least 10 versions. One version of Y function is expected to roughly reach (0,0,0)(1,1,1)(2,2,1)(3,1,0)(2,2,1) in Bashicu matrix system version 2.3 under the assumption of its termination.
Another version of Y function called 0-Y is unexpectedly broken, and hence the limit was considered to correspond to \(\zeta_0\) in fast-growing hierarchy, which is not as big as Yukito had first expected. However, it later turned out to correspond to \(2\) in fast-growing hierarchy.
The limit of another version of Y function called 1-Y is expected to correspond to \(\psi(I)\) with respect to an unspecified ordinal collapsing function in fast-growing hierarchy with respect to an unspecified system of fundamental sequences.
None of those versions of Y function has been formalised yet.
== Termination ==
Yukito conjectured that \(Y(\Omega)+Y_{\omega^3}(Y(\Omega))\) in one version of Y function safely outgrows the limit of Y sequence on 27/02/2020, and hence Y function was supposed to be a quite strong system if it would be completely formalised. However, Yukito noticed that the method applied to S-σ to avoid a certain problem is not applicable to Y function, and hence clarified that he decided to terminate the project to complete the study of Y function on 20/07/2020.
== Sources ==
== See also ==
* side nesting
Category:Functions
Category:Eponymous functions
Category:Side nesting
Category:Unformalised
Category:Googology in Asia
Category:Higher computable level