User blog:MachineGunSuper/A world without the infinite

In this blog post, we will be looking at what would happen if, for some reason, in some unknown way there wouldn't exist infinte ordinals.

The first thing to come up in most people minds would be the fact that the FGH, aswell as the Hardy and Slow Growing hierarchies would be absolutely destroyed.

Without the FGH being able to have infinite ordinals, it would be weak, very weak. In fact, without infinite ordinals the FGH is weaker then up arrow notation.

Second of all, the googological classes would be destroyed. It would become, very, very, very hard or in human terms "Impossible" to approximate some of the bigger numbers on this wiki with the FGH. Now that OCF's are pointless, what could be done?

A potential option would be to use other fast-growing functions, such as BEAF, BAN or HAN. However, as many people agree, it can be difficult to understand array notation mostly because of their messy appearance. We could switch to BMS, but it would be quite difficult to accurately represent numbers.

Uncomputable functions like Rayo(n) or FOOT(n) wouldn't be affected, so not much to cover here.

In a nutshell, chaos would fall upon the world of googology.