Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m: [1]=m ..,[m – 1]=m} =: Zm. %3D

Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m: [1]=m ..,[m – 1]=m} =: Zm. %3D

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
Do item 2 only.
Let m e Zt. Show that =m is an equivalence relation on Z. Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m³ [1]=m; .., [m – 1]=m} =: Zm- Find the elements of [9]=,-
Transcribed Image Text:Let m e Zt. Show that =m is an equivalence relation on Z. Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m³ [1]=m; .., [m – 1]=m} =: Zm- Find the elements of [9]=,-
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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