The bald man paradox is a form of the sorites paradox in which removing one hair is assumed never to make a nonbald person bald. Starting with a nonbald person and repeatedly applying this premise would imply that a person with no hairs is not bald. The difficulty is the premise that a one-hair change can never cross the boundary of the vague predicate "bald," rather than a failure of mathematical induction.
The bald man is one of the seven paradoxes of Eubulides listed by Diogenes Laertius (1925, Book II, §108).
