A fast‑growing hierarchy calculator is more than just a toy—it is a bridge between the abstract world of infinite ordinals and the concrete, mind‑bogglingly large numbers that fascinate googologists and logicians. While the computational explosion inherent in the FGH prevents any calculator from being truly practical for large inputs, the existing implementations in Python, C++, and Lean demonstrate that the hierarchy can indeed be captured by a finite program.
, which represents the first transfinite ordinal), the calculator switches to a specific sequence of functions defined by a choice of fundamental sequences. fω(n)=fn(n)f sub omega of n equals f sub n of n How a Fast-Growing Hierarchy Calculator Functions A digital FGH calculator takes an index and an input
To truly understand the tool, you should build a simple version. This handles only the Wainer hierarchy below ε₀. fast growing hierarchy calculator
Fast-Growing Hierarchy (FGH) is an ordinal-indexed family of rapidly increasing functions,
Press "Expand" or "Compute."
Symbolic/descriptor mode (recommended for larger inputs):
): The starting integer that dictates both the number of function iterations and the resolution of limit ordinals. A fast‑growing hierarchy calculator is more than just
Now wrap your mind around this: ( f_\omega+1(3) ) applies ( f_\omega ) three times, starting from 3. The first ( f_\omega(3) ) is that insane number. Then you apply ( f_\omega ) to that insane number. And then again. The result is barely within the realm of describable googology.
This is the successor function, the fundamental unit of growth. Successor Step fω(n)=fn(n)f sub omega of n equals f sub