The functions in this hierarchy grow extremely rapidly, with F₃(10) already exceeding the number of atoms in the observable universe!
enum Ordinal Zero, Succ(Box<Ordinal>), Limit(Box<dyn Fn(u64) -> Ordinal>), // fundamental sequence Psi(Box<Ordinal>, Box<Ordinal>), // ψ_α(β) Omega, // ω Veblen(Box<Ordinal>, Box<Ordinal>) fast growing hierarchy calculator high quality
: The first level that uses an infinite ordinal. It grows approximately like the , specifically The functions in this hierarchy grow extremely rapidly,
: For a high-quality calculator, the user interface is essential. It should allow users to easily input parameters, select functions from the hierarchy, and visualize the growth of the functions. It should allow users to easily input parameters,
Input: ( \alpha = \omega^\omega ), ( n = 2 ) Step 1: ( f_\omega^\omega(2) = f_\omega^2(2) ) Step 2: ( f_\omega^2(2) = f_\omega\cdot 2(2) ) Step 3: ( f_\omega\cdot 2(2) = f_\omega+2(2) ) Step 4: ( f_\omega+2(2) = f_\omega+1(f_\omega+1(2)) ) ... eventually ( f_2(f_2(2)) = f_2(6) = 2\cdot 6 = 12 )? Wait, check: actually ( f_2(6) = 2^6 \cdot 6? ) No – f_2(n) = (2^n)*n.