Fast Growing Hierarchy Calculator High Quality Info

For $f_\omega(3)$:

Standard recursion $f_\alpha+1(n) = f_\alpha(f_\alpha(...f_\alpha(n)...))$ is computationally infeasible. fast growing hierarchy calculator high quality

Input: ( \alpha = \omega^\omega ), ( n = 2 ) Step 1: ( f_\omega^\omega(2) = f_\omega^2(2) ) Step 2: ( f_\omega^2(2) = f_\omega\cdot 2(2) ) Step 3: ( f_\omega\cdot 2(2) = f_\omega+2(2) ) Step 4: ( f_\omega+2(2) = f_\omega+1(f_\omega+1(2)) ) ... eventually ( f_2(f_2(2)) = f_2(6) = 2\cdot 6 = 12 )? Wait, check: actually ( f_2(6) = 2^6 \cdot 6? ) No – f_2(n) = (2^n)*n. Wait, check: actually ( f_2(6) = 2^6 \cdot 6

): This is the foundation, defined as the : Successor Stage ( fα+1f sub alpha plus 1 end-sub advanced logic for epsilon_0 etc

def fundamental_sequence(self, limit_ordinal, n): # Logic for Wainer Hierarchy if limit_ordinal == 'w': return n # Finite ordinal n if limit_ordinal == 'w*2': return f"w+n" # ... advanced logic for epsilon_0 etc.