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Math Help - Equivalence Class Representatives 2

  1. #1
    is up to his old tricks again! Jhevon's Avatar
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    Equivalence Class Representatives 2

    this thread may come in handy.


    Problem:
    For x,y \in \mathbb{R}, let x \sim y mean x - y is an integer.

    what would be the equivalence class representatives for this?

    Thanks guys
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    by the way, here's the problem that i am having here. we only need one representative from each equivalent class. so i figure 0 could stand in for the integers, since the integers would be one equivalence class. however, i am not sure what would be the representatives for the rationals and irrationals. surely we can't have just one for each set. but there are probably infinitely many equivalence classes for each. i suppose i'd have to describe the set in words, but i can't find the words
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    Grand Panjandrum
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    Quote Originally Posted by Jhevon View Post
    by the way, here's the problem that i am having here. we only need one representative from each equivalent class. so i figure 0 could stand in for the integers, since the integers would be one equivalence class. however, i am not sure what would be the representatives for the rationals and irrationals. surely we can't have just one for each set. but there are probably infinitely many equivalence classes for each. i suppose i'd have to describe the set in words, but i can't find the words
    [0,1)

    RonL
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    [0,1)

    RonL
    haha. well, that was easy!

    i see how that works!

    but please tell me, how did you come up with it? what was your thought process?
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    Grand Panjandrum
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    Quote Originally Posted by Jhevon View Post
    haha. well, that was easy!

    i see how that works!

    but please tell me, how did you come up with it? what was your thought process?
    I can't say, it seemed obvious so maybe I've seen it before?

    RonL
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    I can't say, it seemed obvious so maybe I've seen it before?

    RonL
    you're the man! i'd +rep you if i could, but i gave out too much in the past 24 hrs...

    now that i see the solution, it seems obvious to me as well. i'm so ashamed that i've been racking my brain for days over this. yet i can't explain why it is so obvious... well, maybe i can... i'll think about it. i'll have to explain how to come up with the answer anyway, my professor requires that
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