I request you to please send me the step-by-step solution for the below theorems... Needed to be solved clearly, please... Needed a brief explanation... Theorem. Let a be an irrational number. Then there ezist in finitely many distinct rational numbers : forwhich r-<• Since q grows much more quickly than 2q, this gives us better approximations with smaller denom-inators.

First prove a the following lemma: If n≥1be any integer, then there exists a rationa number pqsuch…

Answered: Theorem. Let z be an irrational number.…

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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Theorem. Let z be an irrational number. Then there exist in finitely many distinct rational numbers for which z-< Since q² grows much more quickly than 2q, this gives us better approximations with smaller denom- inators.