Home of Surveying Specials
This would be the Large Number Enthusiast’s slide rule—a window into the abyss of fast-growing functions.
The hierarchy is built on three simple recursive rules that turn basic addition into "monster" functions:
For those who want to dig into the code, there are several open-source implementations: fast growing hierarchy calculator
To understand how an FGH calculator evaluates outputs, we can trace the lower finite levels of the hierarchy using standard arithmetic operations. Level 0: Linear Growth The base function adds one to the input. Example: Level 1: Multiplication Level 1 nests Level 0 functions times. This results in doubling the input. Formula: Example: Level 2: Exponentiation Level 2 nests Level 1 functions times. This yields an exponential growth curve. Formula: Example: Level 3: Tetration
No real-world computer will ever compute ( f_\omega_1^\textCK(10) ), because that would require solving the halting problem. But we can compute its shape —the skeleton of its growth. And in doing so, we touch something profound: the structure of infinity, made visible through the simple rule of repeated application. This would be the Large Number Enthusiast’s slide
Therefore, architectural implementations do not compute the final digits. Instead, they to find bounds or convert between notations (such as converting Ackerman functions or Knuth up-arrows into their exact FGH equivalents). Comparing FGH to Other Large Number Notations
The fast-growing hierarchy has far-reaching implications in various fields, including: Example: Level 1: Multiplication Level 1 nests Level
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.