Barber Paradox

The Barber Paradox involves a hypothetical barber who shaves everyone in a town who does not shave themselves. The paradox arises when asking: does the barber shave himself? If he does, then by the rule he shouldn't (since he shaves only those who don't shave themselves). If he doesn’t, then he should (since he shaves everyone who doesn’t shave themselves). This creates a logical contradiction, highlighting problems in set definitions and self-reference within naive set theory, and illustrating how certain self-referential rules can lead to paradoxes in formal systems.