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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 $\displaystyle \pi$ 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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