User blog comment:Qq1010903229/Compare These Ordinals Part 1/@comment-44079442-20191222182344

In the non-climbing interpretation (where w^^^...^^^w w/ a ^s for a < w = phi(a-1, 0)), G_0 > {w, w, w} (which is phi(w, 0)), and thus the 2nd and 3rd expressions are equal. phi(e0, 0) is equal to phi(phi(1, 0), 0), which is less than phi(phi(w, 0), 0) which is what {w, 3, 1, 2} would be. However, any sequence that iterates the phi function is limited at G_0 regardless of the starting value, so G_0 = {w, w, 1, 2}.