2.6.4 Let A CR be a non – empty set. Suppose that A is bounded above. Let U = {x E R|x is an upper bound of A}, and let L = R – U. Prove that if x E L and y E U, then x < y.
2.6.4 Let A CR be a non – empty set. Suppose that A is bounded above. Let U = {x E R|x is an upper bound of A}, and let L = R – U. Prove that if x E L and y E U, then x < y.
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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2.6.4
Please include a formal proof.
Transcribed Image Text:2.6.4
Let A SRbe a non –
- empty set. Suppose that A is bounded above.
{x E R|x is an upper bound of A},
and let L = R – U. Prove that if x EL and y E U, then x < y.
Let U =
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