Naive extension

A naive extension is an informal concept cited by Sbiis Saibian,https://sites.google.com/site/largenumbers/home/appendix/a/ulnl2 used to refer to a method of extending a googological system in a way that is obvious and adds no new insight. Specifically, a naive extension of a googological system takes a concept iterated inside that system and lazily applies it again. The Aarex function is an example, which is a naive extension of the Xi function and \(f_{\varphi^{CK}(\omega,0)}(0)\).
Another example is, using the U function:
*\(\{a,b\}_2 = U^b(a)\)
*Other array rules are the same.
*\(U_2(a)\) is defined similiar to U(a), but with 2nd order array notation.
Even though this function grows quite a bit faster, as the growth rate in FGH is doubled, it isn't enough for being prevented from being called a naive extension.
The naive extensions to higher computable fast-growing functions applies including, but not limited to TREE sequence, Subcubic graph number, Busy beaver function, Xi function, Rayo's function, and Loader's function (such as \(D^{99}(99)\) and \(\textrm{Rayo}(\textrm{TREE}(3))\)).
== See also ==
*Salad number
== Sources ==
Category:Concepts