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\iteman{io-port 05252382}
\itemau{Bennett, Charles H.}
\itemti{On random and hard-to-describe numbers.}
\itemso{Calude, Cristian S. (ed.), Randomness and complexity. From Leibniz to Chaitin. Dedicated to Gregory J. Chaitin on the occasion of his 60th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-277-082-0/hbk). 3-12 (2007).}
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Summary: The first essay discusses, in nontechnical terms, the paradox implicit in defining a random integer as one without remarkable properties, and the resolution of that paradox at the cost of making randomness a property which most integers have but can't be proved to have. The second essay briefly reviews the search for randomness in the digit sequences of natural irrational numbers like $\pi$ and artificial ones like Champernowne's $C= 0.12345678910111213\dots$, and discusses at length Chaitin's definable-but-uncomputable number $\Omega$, whose digit sequence is so random that no betting strategy could succeed against it. Other, Cabalistic properties of $\Omega$ are pointed out for the first time.  This paper was written and widely circulated in 1979, but is published here for the first time in its original form.
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