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Thread: Liouville Numbers

  1. #1
    Member Goku's Avatar
    Mar 2011
    South Africa

    Liouville Numbers


    I am trying to prove that e and \pi are not Liouville numbers using Continued Fractions, does anybody know an easy argument of doing this...

    And does any body have an easy way of showing that Liouville Numbers form a strict subset of Transcendental Number

    I know that Any Liouville number must have unbounded partial quotients in its continued fraction expansion. However anybody of a transcendental number that has bounded partial quotients.

    Links to Resources on these will be appreciated.

    Thank You
    Last edited by Goku; Jul 18th 2011 at 08:28 AM.
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