User blog comment:Nedherman1/My Factorial vs HAN!!/@comment-35811215-20180703173610/@comment-30754445-20180705205412

@Cookiefonster

I'm not sure if HAN is well-defined all the way up to what is claimed, but it definitely is way stronger than anything a beginner could conceivably come up with. It does go beyond Γ₀, easily, which is already an insane level of complicated recursion.

There's simply no way to create such numbers unless you're using ordinals (or something equivalent, like carefully set-up trees). I think that BEAF is the largest notation that was ever devised without awareness of ordinals, and even that notation breaks down at ε₀.

A note to the less experienced: To give a glimpse of just how far apart these numbers are from one another, I've created a googological ruler that converts any googolism to a number between 0 to 1000. 'Graham's Number is level 13 and Nedherman's number is at about 15,  but ε₀ is level 50 and Γ₀, is level 100. The claimed limit of HAN (that psi-e-W thingie) is at the 170's, and the strongest array notations ever devised (using highly comlplicated mathematics) are around 260.

Note that the scale is not linear. Progress becomes much much much more difficult, the higher you go.