Wang's Paradox

Theorem

$0$ is a small number.

If $n$ is a small number, then $n + 1$ is a small number.

By the Principle of Mathematical Induction, it follows that all numbers are small numbers.


Resolution

There is no paradox.

Compared to a number which is much greater, every number is a small number.

Besides, small is an imprecise predicate, undefined in mathematics, about which no solid logical conclusions can be inferred.


Source of Name

This entry was named for Hao Wang.


Historical Note

was proposed by Hao Wang as a paradox similar in nature to the sorites.


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Wang's paradox
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