paradox

A paradox is an assertion that is apparently self-contradictory, though based on a valid deduction from acceptable premises.

Paradoxes typically lead to a reevaluation of the axioms of mathematics. Even after axioms are assumed so that the paradox is averted, the statement is still usually referred to as a paradox.

Occasionally, one may refer to a surprising result as a paradox. Such is the case in the birthday paradox, which is not apparently self-contradictory.

Examples of paradoxes include:

• Banach-Tarski paradox
• binary tree paradox
• birthday paradox
• Burali-Forti paradox
• Cantor's paradox
• Hausdorff paradox
• Russell's paradox
• Simpson's paradox
• Zeno's paradox