What does the tilde represent in an equivalence relation on R?

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Homework Help Overview

The discussion revolves around the meaning of the tilde symbol in the context of equivalence relations on the set of real numbers, R. Participants are seeking clarification on its significance and the properties that define such relations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the specific role of the tilde in equivalence relations, expressing uncertainty about its definition. Some participants suggest that it denotes a relationship between elements, while others prompt for foundational properties like reflexivity.

Discussion Status

The conversation is ongoing, with participants exploring the meaning of the tilde and its implications in equivalence relations. There is a request for more information, and some guidance has been offered regarding the properties that need to be demonstrated.

Contextual Notes

Participants have noted the absence of provided equations, which may hinder the discussion's progress. The original poster is working from an attachment that has not been shared in the thread.

Robb
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Homework Statement
Prove that tilde is an equivalence relation on R
Relevant Equations
See attached
Can someone please explain what the tilde represents? We have had no info on this to date. I know it has to do with an equivalence relation but not sure what it represents on its own as in part (a) of the attached. Just want to make sure I'm clear. Thanks!
 

Attachments

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Please post the equations here instead of expecting us to download and open some pdf file.
 
241176
 
Read ##x \sim y ## as "x is related to y".
 
To get you started, you need to show (reflexivity) that x~x or x-x is in ##\mathbb Q ## Can you take it from here?
 

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