User blog comment:Edwin Shade/In The Pursuit Of Organization/@comment-1605058-20171030102151

In the sixth section, you state one thing and prove something completely different. To be fair, I'm not even completely sure what it is that you prove, since your argument doesn't show convergence of the power tower for any \(a\) - just because \(a^x=x\) has a solution (and note you didn't even quite show that), that doesn't imply the sequence \(a,a^a,a^{a^a},\dots\) converges.