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(*) Dirichlet's approximation theorem states that for any real numbers a, ß, ß≥ 1, there exist integers p and q such that 1 ≤q≤ß and qa-pl≤ 1 1 B+1 B (LB denotes the integer part of ß). Prove Dirichlet's approximation theorem with the help of the pigeon hole principle.

(*) Dirichlet's approximation theorem states that for any real numbers a, ß, ß≥ 1, there exist integers p and q such that 1 ≤q≤ß and qa-pl≤ 1 1 B+1 B (LB denotes the integer part of ß). Prove Dirichlet's approximation theorem with the help of the pigeon hole principle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. (*) Dirichlet's approximation theorem states that for any real numbers a, ß, ß ≥ 1, there exist integers p and q such that 1 ≤q≤ß and qa-pl≤- 1 1 < LBJ+1 B (LB denotes the integer part of B). Prove Dirichlet's approximation theorem with the help of the pigeon hole principle.
Transcribed Image Text:6. (*) Dirichlet's approximation theorem states that for any real numbers a, ß, ß ≥ 1, there exist integers p and q such that 1 ≤q≤ß and qa-pl≤- 1 1 < LBJ+1 B (LB denotes the integer part of B). Prove Dirichlet's approximation theorem with the help of the pigeon hole principle.
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