Fast Growing Hierarchy: Calculator !!install!!
Fast-Growing Hierarchy (FGH)
The is a mathematical framework used by googologists and theoretical computer scientists to define and compare functions that grow at staggering rates. It provides a standardized way to describe "ridiculously huge numbers" using ordinals to index the level of growth complexity. 🛠️ Core Definition The hierarchy consists of an indexed family of functions
f sub alpha colon the natural numbers right arrow the natural numbers fast growing hierarchy calculator
return "Unknown Ordinal"
comparison
, 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? Fast-Growing Hierarchy (FGH) The is a mathematical framework
This would be the Large Number Enthusiast’s slide rule—a window into the abyss of fast-growing functions. Finite and small ordinals: 0, 1, 2, …,
print(fgh(2, 3)) # Output: 24 print(fgh('w', 2)) # Output: fgh(2,2) = 8
- Finite and small ordinals: 0, 1, 2, …, ω, ω+1, ω·2, ω^2, ε0.
- Ordinal notations to include: Cantor normal form (CNF) for ordinals < ε0; fundamental sequences for limit ordinals below ε0.
- Reasonable cutoff: support up to ε0 for practical computation and representation. Beyond ε0 requires more advanced notation (Veblen, collapsing functions).