All right I REALLY need help. I've asked a bunch of people and just don't get it.
I understand equivalence relations. They seem easy enough, I can deal with them.
But here's a problem I really need help with:
a,b elements_of Z
aRb IFF a%n = b%n = 0
How do i get an equivalence class for this, I'm in desperate need of help!
and PS I've worked out a few pages of attempts, and the mostly end up with a = a
so sorry! I guess our teacher uses some strange notation.
Ok a and b are elements of Z (the integers, +-)
n is a integer
aRb = a Related b iff (a mod n = 0 = b mod n)
it's an equivalence relation.
how do i go about creating an equivalence class for this relation?
means that and are both divisible by . But it's not clear how is defined. After all, for all , so . So we need to know something else about .
In the meantime, you might find the following post helpful if you want a couple of illustrations of equivalence classes: http://www.mathhelpforum.com/math-he...relations.html.
PS In fact, unless it is not an equivalence relation, because ; in other words is a factor of every integer, which is nonsense.