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    Real Single-Variable Analysis Problem

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    Let x be an irrational number. Prove that there exist infinitely many fractions (p/q) with p and q as integers such that:

    abs(x-[p/q]) < 1/(q^2)

    © BrainMass Inc. brainmass.com November 30, 2021, 12:16 am ad1c9bdddf
    https://brainmass.com/math/real-analysis/real-single-variable-analysis-problem-31519

    Solution Summary

    A real single-variable analysis is examined. The expert proves that there exists infinitely many fractions.

    $2.49

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