paradox
Paradox
2006-07-30 15:07:34
2007-05-14 17:43:23
Definition
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A {\sl 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. \PMlinkescapetext{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:
\begin{itemize}
\item Banach-Tarski paradox
\item binary tree paradox
\item \PMlinkname{birthday paradox}{BirthdayParadox}
\item Burali-Forti paradox
\item Cantor's paradox
\item Hausdorff paradox
\item Russell's paradox
\item Simpson's paradox
\item Zeno's paradox
\end{itemize}