Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Question 8. The usual order relation > on R satisfies the two conditions (a) if x 0, then precisely one of x > 0 or -x > 0 holds; and (b) if x, y> 0, then x + y> 0 and xy > 0. Show that there does not exist a relation > on C which satisfies both these conditions. Thus there is no natural ordering on the complex numbers. Inequalities hold between real numbers, as usual, but no meaningful inequalities hold between complex numbers.

Question 8. The usual order relation > on R satisfies the two conditions (a) if x 0, then precisely one of x > 0 or -x > 0 holds; and (b) if x, y> 0, then x + y> 0 and xy > 0. Show that there does not exist a relation > on C which satisfies both these conditions. Thus there is no natural ordering on the complex numbers. Inequalities hold between real numbers, as usual, but no meaningful inequalities hold between complex numbers.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Question 8. The usual order relation > on R satisfies the two conditions (a) if x # 0, then precisely one of x > 0 or −x > 0 holds; and (b) if x, y > 0, then x + y > 0 and xy > 0. Show that there does not exist a relation > on C which satisfies both these conditions. Thus there is no natural ordering on the complex numbers. Inequalities hold between real numbers, as usual, but no meaningful inequalities hold between complex numbers.
Transcribed Image Text:Question 8. The usual order relation > on R satisfies the two conditions (a) if x # 0, then precisely one of x > 0 or −x > 0 holds; and (b) if x, y > 0, then x + y > 0 and xy > 0. Show that there does not exist a relation > on C which satisfies both these conditions. Thus there is no natural ordering on the complex numbers. Inequalities hold between real numbers, as usual, but no meaningful inequalities hold between complex numbers.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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,
SEE MORE TEXTBOOKS