Answered: Let R= {(x, e¹x) : xER, n = Z}. Here e…

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.

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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Question

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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Follow-up Questions

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Follow-up Question

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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Follow-up Question

hello, can you explain how it is symmetric in more detail?

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