1. ## Equivalence Class HELP!

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!

Thank you.

and PS I've worked out a few pages of attempts, and the mostly end up with a = a

2. Originally Posted by kodai
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!

Thank you.

and PS I've worked out a few pages of attempts, and the mostly end up with a = a
Here is some bad news for you.
What in the world does "aRb IFF a%n = b%n = 0" mean?
Please repost the question using standard mathematical symbols.

3. 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?

4. ## Equivalence Classes

Hello kodai
Originally Posted by kodai
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?
I'm not sure that I understand the question.

$(a \mod n = 0 = b \mod n)$ means that $a$ and $b$ are both divisible by $n$. But it's not clear how $n$ is defined. After all, $a \mod 1 =0$ for all $a$, so $n=1 \Rightarrow \forall a, b, aRb$. So we need to know something else about $n$.

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 $n=1$ it is not an equivalence relation, because $(aRa \Rightarrow a \mod n = 0) \Rightarrow n|a, \forall a \in \mathbb{Z}$; in other words $n$ is a factor of every integer, which is nonsense.