If you did compute ( f_\omega+1(4) ) as an integer, you’d need more than ( 10^100 ) bits of memory—physically impossible. Hence any honest FGH calculator never expands to a full integer; it stays in a compressed symbolic form unless the result is tiny.
An FGH calculator is not a tool you use to balance your checkbook. It is a conceptual (and sometimes actual) piece of software designed to compute—or at least approximate—functions that grow faster than any human intuition can follow. Building one is a journey into the foundations of computation, ordinal notations, and the very meaning of "infinity." fast growing hierarchy calculator
: While technically for the Hardy hierarchy (closely related to FGH), this HardyCalc tool ExpantaNum.js If you did compute ( f_\omega+1(4) ) as
# Increase recursion depth for deep hierarchical calls sys.setrecursionlimit(2000) It is a conceptual (and sometimes actual) piece
This is the successor function, the fundamental unit of growth. Successor Step