# Equivalence Class Representatives 2

• Feb 18th 2008, 11:48 PM
Jhevon
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
• Feb 19th 2008, 11:51 AM
Jhevon
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, 03:30 PM
CaptainBlack
Quote:

Originally Posted by Jhevon
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
• Feb 19th 2008, 03:32 PM
Jhevon
Quote:

Originally Posted by CaptainBlack
[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?
• Feb 19th 2008, 03:45 PM
CaptainBlack
Quote:

Originally Posted by Jhevon
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
• Feb 19th 2008, 03:48 PM
Jhevon
Quote:

Originally Posted by CaptainBlack
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