User blog comment:Edwin Shade/In The Pursuit Of Organization/@comment-1605058-20171030102151/@comment-32876686-20171031175428

I believe I understand now the issue, but proving $$x^{x^{x^{.^{.^{.}}}}}$$ converges when $$x\neq 1$$ will be difficult, because I'm not sure how to even go about proving it. Still, I'll try to make a proper proof of it.