User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190718022500/@comment-31580368-20190718075203

Yes, x is free variable of the functions. I thought that if the right side diverges, then the limit = ∞, but  the limit of the left side will always be a finite number →0. But it seems I hurried with the definition, really we are dependent on fundamental sequences and it's can disconverge both parts.

Anyway, thanks for the constructive discussion, and for multiple attempts to restore order in googology.