The Suslin conjecture is a hypothesis in set theory that deals with the properties of certain types of ordered sets, specifically well-ordered sets. It posits that every well-ordered set of real numbers can be represented as a countable union of countable sets. This conjecture is significant in the study of cardinal numbers and the structure of real numbers. The conjecture was proposed by the mathematician Mikhail Suslin in the early 20th century. It has implications for the understanding of continuum hypothesis and the nature of infinite sets. Despite extensive research, the conjecture remains unresolved in the context of Zermelo-Fraenkel set theory with the Axiom of Choice.