# Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche

@article{HurwitzUeberDA,
title={Ueber die angen{\"a}herte Darstellung der Irrationalzahlen durch rationale Br{\"u}che},
journal={Mathematische Annalen},
volume={39},
pages={279-284}
}
• A. Hurwitz
• Published 1 June 1891
• Mathematics
• Mathematische Annalen
Man kann bekanntlich jede Irrationalzahl a durch eine unbegrenzte Reihe von rationalen Bruchen $$\frac{{{x_1}}}{{{y_1}}},\;\frac{{{x_2}}}{{{y_2}}},\;\frac{{{x_3}}}{{{y_3}}},\; \ldots$$ (1) derart annahern, dass, abgesehen vom Vorzeichen, $$\alpha- \frac{{{x_n}}}{{{y_n}}}< \frac{1}{{y_n^2}}\quad \left( {n = 1,\;2,\;3 \ldots } \right)$$ (2) ist. Dieser Satz ergibt sich unmittelbar aus der Lehre von den Kettenbruchen; er lasst sich aber auch durch andere sehr…

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