fα+1(n)=fαn(n)f sub alpha plus 1 end-sub of n equals f sub alpha to the n-th power of n The function at the next stage nests the current function times. For example,
Zero is treated as the base case. $$f_0(n) = n + 1$$ fast growing hierarchy calculator
The hierarchy can theoretically expand forever. However, once indexing reaches the Church-Kleene ordinal ( ω1CKomega sub 1 raised to the cap C cap K power fα+1(n)=fαn(n)f sub alpha plus 1 end-sub of n
: There is no "single" way to define these for very high ordinals, leading to different "standards" (like the Wainer hierarchy). However, once indexing reaches the Church-Kleene ordinal (
, it is mathematically more powerful than almost anything encountered in standard calculus or physics. To help you dive deeper into specific growth rates: Do you need a between FGH and Hardy hierarchies? Should I explain specific ordinals like ζ0zeta sub 0 or the Feferman-Schütte ordinal?
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