If you are testing an online tool or a script you found on GitHub, use these benchmark calculations to verify its quality and accuracy: : Ensure equals 6, the successor rule is working. The Test : Ensure . For example, The Test : shifts into hyperoperations (exponential towers). should equal The Boundary : Enter . A high-quality calculator will correctly expand this to based on the standard fundamental sequence , outputting
(the limit of Peano Arithmetic) and the Feferman-Schütte ordinal Γ0cap gamma sub 0 How to Verify the Quality of an FGH Calculator fast growing hierarchy calculator high quality
def fgh(n, x): """ A basic FGH calculator for finite levels. n: The hierarchy index (layer) x: The input value """ if n == 0: return x + 1 # Iterate the previous level x times result = x for _ in range(x): result = fgh(n - 1, result) return result # Example: Compute f_2(3) -> 3 * 2^3 = 24 print(f"f_2(3) = fgh(2, 3)") Use code with caution. If you are testing an online tool or
While Ackermann's function and Conway chained arrows can describe massive numbers, the FGH unifies them into a single, scalable hierarchy. If a number can be defined by an algorithm, the FGH can categorize exactly how fast that definition grows. How the Hierarchy Accumulates Value should equal The Boundary : Enter
As googology advances, so do the tools. Future high-quality FGH calculators will likely focus on several key areas:
Standard definition (for ( n \ge 1 )):