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

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The tilde symbol (~) in an equivalence relation on R indicates that two elements, x and y, are related, expressed as "x is related to y." The discussion emphasizes the need for clarity on this notation, particularly in the context of demonstrating reflexivity, which requires showing that x~x holds true. Participants are encouraged to provide equations directly in the forum instead of linking to external files. The initial query seeks a foundational understanding of the equivalence relation and its properties. Overall, the conversation highlights the importance of grasping the concept of equivalence relations in mathematical contexts.
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!
 

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Please post the equations here instead of expecting us to download and open some pdf file.
 
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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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