Fast Growing Hierarchy Calculator Fixed May 2026
The Fast-Growing Hierarchy (FGH) 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
A common choice is Cantor normal form:
( \alpha = \omega^\beta_1 \cdot c_1 + \dots + \omega^\beta_k \cdot c_k ) with ( \beta_1 > \dots > \beta_k ). fast growing hierarchy calculator
Part 4: Why Can’t a Normal Computer Calculate Large FGH?
If you try to compute ( f_ω+1(4) ) on a standard calculator, it will crash, overflow, or freeze. Why? The Fast-Growing Hierarchy (FGH) is a mathematical framework
- F1(n) = n + 1 (a simple increment function)
- F2(n) = 2n (a linear function)
- F3(n) = 2^n (an exponential function)
- F4(n) = 2^(2^n) (a double exponential function)
- F5(n) = 2^(2^(2^n)) (a triple exponential function)
1. Ordinal Representation
Ordinals are not integers. The calculator must support: Overflow handling: A common choice is Cantor normal
- Use a loop or recursion: Implement the calculator using a loop or recursive function to compute the results.
- Support multiple functions: Allow users to select from a range of functions, including non-standard ones.
- Visualize growth rates: Provide a graph or chart to illustrate the growth rates of the functions.
- Handle large inputs: Be prepared to handle large input values, which may require special handling to avoid overflow or performance issues.