# 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)

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:56 am ad1c9bdddfhttps://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