User blog comment:MachineGunSuper/Question/@comment-34804556-20180224153034

Artism is right, the FGH can extend infinitely farther as long as the fundamental sequences for the ordinals in the subscript are well-defined. In addition, the fast growing hierarchy can be used, and is commonly used, to stratify difference growth rates of notations such as BEAF, so that it serves as a mathematical ruler.