Snap Project with the expansions: https://snap.berkeley.edu/embed?projectname=ε_0%20in%20Snap!%20(ACTUAL)&username=polymations&showTitle=true&editButton=true
I realized if we change the last rule of the system to instead subtracting everything after the 1 in the bad part subtracted by 1, expanding that, and then adding it by one again, we can achieve $$\varepsilon_0$$! Although it's just a small change, it achieves what I originally wanted! Epsilon 0 without nesting lists! Note that some of the arrays that were valid in V1 aren't valid in V2. For example, 1,3 can't be expanded because then you have to expand the "3" part, and it can't expand. This means that in a sequence, each next number can't be added by a number more than one, but can be subtracted by a number equal to or greater than zero.1,2,3,4,5,6,7,8,9,10,... is $$\varepsilon_0$$. The new script:
Because i don't know how. However, I'm thinking of making a pair sequence version, which Pair sequence system itself (the googology one by BashicuHydora) is $$\psi(\Omega_\omega)$$, beyond any of these ordinals possible. In fact, the Small veblen ordinal, which in FGH is about TREE(n), is just $$\psi(\Omega^{\Omega^\omega})$$!
