function evaluate_FGH(ordinal, input_n): if ordinal == 0: return input_n + 1 elif is_successor(ordinal): previous_ordinal = ordinal - 1 current_value = input_n for i from 1 to input_n: current_value = evaluate_FGH(previous_ordinal, current_value) return current_value elif is_limit(ordinal): resolved_ordinal = get_fundamental_sequence(ordinal, input_n) return evaluate_FGH(resolved_ordinal, input_n) Use code with caution.
When evaluating a limit ordinal at a specific argument
: Pentational growth. This level easily generates , which sits comfortably below Transfinite Ordinals: Entering the Infinite When the index reaches
The Fast-Growing Hierarchy is a structured family of fast-growing functions indexed by ordinal numbers. It simplifies the classification of large numbers by grouping them based on their rate of growth. As the index (usually denoted by the Greek letter alpha, fast growing hierarchy calculator
(Using a "fundamental sequence" to approximate infinite ordinals). 🚀 Growth Milestones As the index increases, the functions quickly surpass common operations:
A typical takes:
This public link is valid for 7 days and shares a thread, including any personal information you added. This link or copies made by others cannot be deleted. If you share with third parties, their policies apply. Can’t copy the link right now. Try again later. It simplifies the classification of large numbers by
: The Epsilon-zero level, which bounds the provably total functions of Peano Arithmetic and characterizes numbers like Graham's Number. Mapping Famous Large Numbers to FGH
The most prominent online calculator is the . This JavaScript tool allows you to input a natural number (n) and a countable ordinal (\alpha) expressed in the normal form for the Extended Buchholz function, a powerful system of fundamental sequences that reaches far beyond the small Veblen ordinal. It is one of the few calculators that can handle ordinals beyond (\varepsilon_0). Another notable tool is the Ordinal Expander in JavaScript (ordex) , which is designed to expand ordinals and compute their fundamental sequences, which is the core operation for any FGH calculator.
The fast growing hierarchy is a mathematical concept that describes a sequence of functions that grow extremely rapidly. These functions are often used to demonstrate the limits of mathematical notation and to explore the boundaries of computability. In this article, we will introduce the fast growing hierarchy calculator, a tool that allows users to compute and visualize these rapidly growing functions. This link or copies made by others cannot be deleted
if alpha_in == 'w': alpha_val = 'w' else: alpha_val = int(alpha_in)
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