User blog comment:Edwin Shade/In The Pursuit Of Organization/@comment-1605058-20171030102151/@comment-32876686-20171030175943

@LittlePeng9

I believe your example didn't work because $$1+1-1+1-1+...$$ isn't well defined enough.

Also, though I forgot to add this, I should add that there is a minimum a such that there is no solution for x in $$a=x^{x^{x^{.^{.^{.}}}}}$$, just as there is an upper finite bound for a, there is a lower finite bound for a. a can never be finite if $$x\geq e^{\frac{1}{e}}$$ but that does not imply a is finite just because x is less than $$e^{\frac{1}{e}}$$.

There is a finite range of values such that a is finite.