Bertrand Russell's paradox

Bertrand Russell's paradox highlights a fundamental problem in set theory regarding self-referential sets. Consider a set that contains all sets that do not contain themselves. If this set includes itself, it contradicts its own definition. Conversely, if it does not include itself, it should include itself according to its own rule. This paradox reveals inconsistencies in naive set theory, prompting the development of more rigorous foundations in mathematics to avoid such contradictions, influencing modern logic and philosophy profoundly. It illustrates the complexities of self-reference and the challenges of defining collections or sets.