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Theorem (Hurwitz, 1891). Let z be irational. Then there are in finitely many distinct rational numbers for which Proof. This needs more advanced number theory. (But proving that this inequality is strict, i.e., that 5 cannot be increased, would be hard but feasible.)

Theorem (Hurwitz, 1891). Let z be irational. Then there are in finitely many distinct rational numbers for which Proof. This needs more advanced number theory. (But proving that this inequality is strict, i.e., that 5 cannot be increased, would be hard but feasible.)

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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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 (Hurwitz, 1891). Let z be irrational. Then there are in finitely many distinct rat ional numbers 2 for which Proof. This needs more advanced number theory. (But proving that this inequality is strict, i.e., that 5 cannot be increased, would be hard but fea si ble.)
Transcribed Image Text:Theorem (Hurwitz, 1891). Let z be irrational. Then there are in finitely many distinct rat ional numbers 2 for which Proof. This needs more advanced number theory. (But proving that this inequality is strict, i.e., that 5 cannot be increased, would be hard but fea si ble.)
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