Russell's Paradox

Russell's Paradox highlights a contradiction in set theory, which is a fundamental part of mathematics. It questions whether the set of all sets that do not contain themselves contains itself. If it does, it shouldn't, because it only includes sets that don’t include themselves. If it doesn't, then it must, as it qualifies as a set not containing itself. This paradox reveals limitations in naive set theory and led to the development of more rigorous foundations in mathematics to avoid such contradictions. It illustrates how self-referential concepts can lead to logical inconsistencies.