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naive extension is an informal concept cited by Sbiis Saibian,[1] 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.

See also

Sources

  1. https://sites.google.com/site/largenumbers/home/appendix/a/numbers2
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