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From a ball game to incompleteness

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Abstract

We present a ball game that can be continued as long as we wish. It looks as though the game would never end. But by applying a result on trees, we show that the game nonetheless ends in some finite number of moves. We then point out some deep results on the natural number system connected with the game.

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Suggested Reading

  1. R M Smullyan, A Beginner’s Guide to Mathematical Logic, Dover, 2014.

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  2. A Singh, Logics for Computer Science, 2nd Ed, To appear, PHI, 2018.

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Authors and Affiliations

  1. Department of Mathematics, IIT Madras, IT P.O., Chennai, 600 036, India

    Arindama Singh

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  1. Arindama Singh
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Correspondence to Arindama Singh.

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Arindama Singh works as a Professor in Mathematics at IIT Madras. His teaching and research interests include theory of computation, logic, and linear algebra. He has authored three books in these areas.

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Singh, A. From a ball game to incompleteness. Reson 22, 1205–1211 (2017). https://doi.org/10.1007/s12045-017-0582-y

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  • DOI: https://doi.org/10.1007/s12045-017-0582-y

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