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econstruct the proof of the following statement: The supremum of a bounded from above subset A of R is unique. Proof. We do a proof by . Assume that x₁ and x2 are both supremum of A with x₁ for all e> 0 there exists x EA such that x x₁.This proves that x₁ is not an x2. Since x₂ = . It follows that there exists x EA such that x our hypothesis. upper bound contradiction sup(A) # X_2-x_1>0 equal to x2. We can assume that x₁ X2-6. Choose, e for A in different from with

econstruct the proof of the following statement: The supremum of a bounded from above subset A of R is unique. Proof. We do a proof by . Assume that x₁ and x2 are both supremum of A with x₁ for all e> 0 there exists x EA such that x x₁.This proves that x₁ is not an x2. Since x₂ = . It follows that there exists x EA such that x our hypothesis. upper bound contradiction sup(A) # X_2-x_1>0 equal to x2. We can assume that x₁ X2-6. Choose, e for A in different from with

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 18E: Show that the converse of Eisenstein’s Irreducibility Criterion is not true by finding an...
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Reconstruct the proof of the following statement: The supremum of a bounded from above subset A of R is unique. Proof. We do a proof by Assume that x₁ and x2 are both supremum of A with x₁ for all e> 0 there exists x E A such that x x₁.This proves that x₁ is not an x2. Since x₂ = It follows that there exists x EA such that x our hypothesis. upper bound contradiction sup(A) # X_2-x_1>0 equal to X2. We can assume that x₁ X2 - E. Choose, e for A in different from with
Transcribed Image Text:Reconstruct the proof of the following statement: The supremum of a bounded from above subset A of R is unique. Proof. We do a proof by Assume that x₁ and x2 are both supremum of A with x₁ for all e> 0 there exists x E A such that x x₁.This proves that x₁ is not an x2. Since x₂ = It follows that there exists x EA such that x our hypothesis. upper bound contradiction sup(A) # X_2-x_1>0 equal to X2. We can assume that x₁ X2 - E. Choose, e for A in different from with
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