Abstract
Given a real number α, let [α], the integer part of α, denote the greatest integer ≤ α, and let {α} = α − [α]. Then {α} is the fractional part of α, and satisfies 0 ≤ {α} < 1. Also, let ‖α‖ denote the distance from α to the nearest integer. Then always 0 ≤ ‖α‖ ≤ 1/2.
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References
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© 1980 Springer-Verlag Berlin Heidelberg
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(1980). Approximation to Irrational Numbers by Rationals. In: Diophantine Approximation. Lecture Notes in Mathematics, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38645-2_1
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DOI: https://doi.org/10.1007/978-3-540-38645-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09762-4
Online ISBN: 978-3-540-38645-2
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