this thread may come in handy.

Problem:

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

what would be the equivalence class representatives for this?

Thanks guys

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- Feb 18th 2008, 10:48 PMJhevonEquivalence Class Representatives 2
this thread may come in handy.

__Problem:__

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

what would be the equivalence class representatives for this?

Thanks guys - Feb 19th 2008, 10:51 AMJhevon
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

- Feb 19th 2008, 02:30 PMCaptainBlack
- Feb 19th 2008, 02:32 PMJhevon
- Feb 19th 2008, 02:45 PMCaptainBlack
- Feb 19th 2008, 02:48 PMJhevon
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