 Paradoxes of naive set theory

Naive set theory is a branch of set theory that deals with sets and their properties without the formal rigor of axiomatic set theories, such as Zermelo-Fraenkel set theory (ZF) or Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). While naive set theory is intuitive and allows for straightforward manipulation of sets, it leads to several paradoxes due to its lack of formal restrictions.