Classify the continuum as a successor or limit cardinal in ZFC

Ascertain, within Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC), whether the cardinality of the continuum 𝔠 is a successor cardinal (of the form κ^+) or a limit cardinal.

Background

The author summarizes known facts about various cardinals and observes that, relative to the axioms of ZFC alone, it is unresolved whether the continuum 𝔠 (the cardinality of the real numbers) is a successor cardinal or a limit cardinal.

This classification is intertwined with the continuum hypothesis and its generalizations, which are independent of ZFC; nevertheless, the specific successor-or-limit status of 𝔠 in ZFC remains undetermined.