Discrete Math sample 6. (*) Dirichlet's approximation theorem states that for any real numbers a, ß, ß ≥ 1, thereexist integers p and q such that 1 ≤q≤ß andqa-pl≤-11<LBJ+1 B(LB denotes the integer part of B).Prove Dirichlet's approximation theorem with the help of the pigeon hole principle.

Given: Dirichlet's Approximation Theorem: Dirichlet's approximation theorem states that for any real…

Answered: (*) Dirichlet's approximation theorem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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.