User blog comment:Sbiis Saibian/Googology101 - Part II/@comment-10429372-20141024190431/@comment-2033667-20141025064139

\(\lim_{n\mapsto\inf} x\uparrow\uparrow n = -\frac{W(-\ln x)}{\ln x}\) Actually, no. The definition of the limit would imply that the limit is divergent, at least for x = 10. Limits are not multivalued either, which makes this incompatible with the W function,