Exercise 6. Let ECR such that E is nonempty and bounded. Prove that the set -E= {-x : x E E} satisfies inf(E) = – sup(-E).
Exercise 6. Let ECR such that E is nonempty and bounded. Prove that the set -E= {-x : x E E} satisfies inf(E) = – sup(-E).
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 and 7
Transcribed Image Text:Exercise 6. Let ECR such that E is nonempty and bounded. Prove that the set -E={-x :x E
E} satisfies inf(E):
– sup(-E).
Exercise 7. If x is a rational number and y is irrational, prove that x +
and x- y are irrational.
Exercise 8. If x, y ER with x < y, prove that x < tx + (1- t)y <y for all t E (0, 1).
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