Quality — Fast Growing Hierarchy Calculator High

def f(alpha, n): if alpha == 0: return n+1 val = n for _ in range(n): val = f(alpha-1, val) return val

Common choice (Wainer hierarchy):

is a . High-quality calculators use these three fundamental rules: fast growing hierarchy calculator high quality

(α+ωγ+1)[n]=α+ωγ⋅nopen paren alpha plus omega raised to the gamma plus 1 power close paren open bracket n close bracket equals alpha plus omega raised to the gamma power center dot n def f(alpha, n): if alpha == 0: return

Historically used as an upper bound in prime number mathematics. This yields standard exponential growth

f2(n)=f1n(n)=2×2×…×2×n=n⋅2nf sub 2 of n equals f sub 1 to the n-th power of n equals 2 cross 2 cross … cross 2 cross n equals n center dot 2 to the n-th power For an input of 5, . This yields standard exponential growth. Level: Tetration and Towering Iterating exponential growth leads to towers of exponents: