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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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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: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.
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.
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.
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