User blog comment:O0112111/Is w^2 a fixed poit of w+a=a?/@comment-35470197-20190614121128/@comment-30004975-20190618182507

e0 is the smallest ordinal such that a=w^a. w^^w=w^(w^^w). Thus, w^^w=e0. You can also do e0^^w=e1, e1^^w=e2... However, higher tetponents (w^^(w+1)) or higher hyperoperators (w^^^w) quickly run into problems (what does a power tower of height w+1 even mean?). They can be resolved in many ways, but depending on who you ask w^^(w+1) can be as low as e0*w or as high as ew. (All but the strongest approach converge at w^^^w=z0, but w^^(w+1)=ew says that w^^w^2=z0 and w^^^w=g0.)