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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
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
Expert Solution
Step 1

Advanced Math homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,