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. 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 (http://planetmath.org/BirthdayParadox)

• Burali-Forti paradox

• Cantor’s paradox

• Hausdorff paradox

• Russell’s paradox

• Simpson’s paradox

• Zeno’s paradox