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Let m e Z+. Show that =m is an equivalence relation on Z. Prove that for any integer a,

Let m e Z+. Show that =m is an equivalence relation on Z. Prove that for any integer a,

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
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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]=,-
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