Let SC R. Show that z E Siff Please follow steps: inf {|r- s | s € S} = 0. Let x € 3 and let € > 0. Explain why for € > 0, D(x, €) Ns 0. Take s E D (1,€) S and explain why 0 ≤ inf{|rs|s € S} < €. Why can we conclude that inf {|rs|s € S} = 0.
Let SC R. Show that z E Siff Please follow steps: inf {|r- s | s € S} = 0. Let x € 3 and let € > 0. Explain why for € > 0, D(x, €) Ns 0. Take s E D (1,€) S and explain why 0 ≤ inf{|rs|s € S} < €. Why can we conclude that inf {|rs|s € S} = 0.
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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Question
Please follow the steps to answer the question and fill in all the required spaces. Thanks
Transcribed Image Text:Let S CR. Show that Siff
Please follow steps:
inf {|rs| s € S} = 0.
Let S and let e > 0. Explain why for € > 0,
D(x, €) ns +0.
Take s E D (x, €) nS and explain why
0 ≤ inf {|rs| | 8 € S} < €.
-
Why can we conclude that
inf {|xs| 8 € S} = 0.
Transcribed Image Text:Why can we conclude that
Conversely, assume that
inf {|rs|s € S} = 0.
inf {|rs|s € S} = 0.
Take € > 0 and explain why there is s ES, such that
|xs| < €.
Conclude that
Explain why we can find s € SnD (™, €).
D(x, €) ns 0.
Explain why we can say that ze S.
Expert Solution
Step 1: Conceptual understanding
iff
To show that if and only if , we'll go through the following steps:
Let and let
By definition, is in the closure of () if every open ball centered at with radius intersects .
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