User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190718022500/@comment-35470197-20190718091007

> the right side diverges, then the limit = ∞,

Usually true. But the right hand side might behave like a sine curve, because FGH is not necessarily strictly increasing.

> the limit of the left side will always be a finite number →0.

Usually true. But the left hand side might converge to a positive real number.

> really we are dependent on fundamental sequences and it's can disconverge both parts.

Right. The behaviour of FGH heavily depends on the system of fundamental sequences, and is quite difficult to control in a theoretic way. We just believe that FGH generates sufficiently strong functions.

It is my pleasure. Please do not hesitate to ask googological questions.