By the time we reach ( f_\omega(n) ) (where ( \omega ) is the first infinite ordinal), we’ve surpassed primitive recursive functions. By ( f_\omega+1(n) ), we’re in the realm of the Ackermann function. And then it gets fast .
Navigating Infinity: A Comprehensive Guide to Fast-Growing Hierarchies and Computational Googology
FGH is used to classify the complexity of algorithms. If an algorithm's running time grows at the rate of fast growing hierarchy calculator
yields an exponent tower of 2s that is thousands of levels high.
Despite their theoretical simplicity, creating a practical FGH calculator faces huge obstacles: By the time we reach ( f_\omega(n) )
function to find the FGH equivalent of a given large number. Ordinal Calculator and Explorer : A blog-based project on the Googology Wiki
print(f"\nCalculating f_alpha_val(n_in)...") Ordinal Calculator and Explorer : A blog-based project
In mathematical logic, ordinals measure the strength of mathematical proof systems. FGH connects these abstract proof strengths directly to rapidly growing arithmetic functions.
To build the calculator, we must define the hierarchy mathematically.