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Approximation of Irrational Numbers

In: Markov's Theorem and 100 Years of the Uniqueness Conjecture

Author

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  • Martin Aigner

    (Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik)

Abstract

Our story begins with one of the oldest questions in number theory: How well can a real number be approximated by rational numbers? Phrased in this way, the answer is “arbitrarily well,” since every real number α is the limit of a sequence $$(\frac{p_n}{q_n})$$ of rationals. But in such a convergent sequence, e.g., the decimal expansion of an irrational number α, the denominators usually grow very fast

Suggested Citation

  • Martin Aigner, 2013. "Approximation of Irrational Numbers," Springer Books, in: Markov's Theorem and 100 Years of the Uniqueness Conjecture, edition 127, chapter 1, pages 3-29, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00888-2_1
    DOI: 10.1007/978-3-319-00888-2_1
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