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Let R= {(x, e¹x) : xER, n = Z}. Here e = 2.71828... as usual.) Prove that R is an equivalence relation on the set of real umbers.

Let R= {(x, e¹x) : xER, n = Z}. Here e = 2.71828... as usual.) Prove that R is an equivalence relation on the set of real umbers.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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Let R: = {(x,e¹x) : x ≤R,n≤ Z}. Here e = 2.71828... as usual.) Prove that R is an equivalence relation on the set of real umbers.
Transcribed Image Text:Let R: = {(x,e¹x) : x ≤R,n≤ Z}. Here e = 2.71828... as usual.) Prove that R is an equivalence relation on the set of real umbers.
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If (x,y) = (x,enx), with x = 'x', and y = 'enx', I understand that (y,z) = (enx,z). I don't understand why z has to = emx.ex. I don't know why it cant just be (enx, emx). If we want to conclude m+n € Z, why cant we just say m € Z and not have to do e emx.enx? E I would like some help understanding, thank you.
Transcribed Image Text:If (x,y) = (x,enx), with x = 'x', and y = 'enx', I understand that (y,z) = (enx,z). I don't understand why z has to = emx.ex. I don't know why it cant just be (enx, emx). If we want to conclude m+n € Z, why cant we just say m € Z and not have to do e emx.enx? E I would like some help understanding, thank you.
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hello, can you explain how it is symmetric in more detail?

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