I just realised it could also mean the entirety of a set with an infinite cardinality.

But we don't have enough evidence to conclude the cardinality of fuckery. And if the cardinality is not the same, there can't be a bijection and therefore also no isomorphism between two groups.

An "entire" fiction is analytic at all points on the complex plane, so by Liouville's boundedness theorem, it is either constant or unbounded. I think we can agree that this fuck function isn't constant, so it must be unbounded. It is also continuous, thus infinite.