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A naive extension is an informal concept devised by Sbiis Saibian, 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:

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  • Naive extension
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  • A naive extension is an informal concept devised by Sbiis Saibian, 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:
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  • A naive extension is an informal concept devised by Sbiis Saibian, 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.
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