Originally Posted by

**Meelas** Wazzup,

I hope that everybody is A+ up in here.

Check it:

I have have a subset $\displaystyle Q$ of $\displaystyle \mathbb{Z} \times \mathbb{Z}$ :

$\displaystyle Q=\left\lbrace \left( a,b \right)\in \mathbb{Z}\times \mathbb{Z}\mid b \neq 0\right\rbrace $

I have a relation $\displaystyle \sim$ defined on $\displaystyle Q$:

$\displaystyle \left( a,b \right) \sim \left( c,d \right)\Leftrightarrow ad=bc $

I've shown that the relation is an equivalence-relation.

Now I wanna "find" $\displaystyle \left[ (2,3)\right]$ and in general $\displaystyle \left[ (a,b)\right]$.

Is the following enough:

The equivalence class $\displaystyle \left[ (2,3)\right] $ consists of all pairs of numbers $\displaystyle (c,d)$ such that $\displaystyle 2d=3c$, meaning $\displaystyle \left[ (2,3) \right]= \left\lbrace (c,d) \mid 2d=3c \right\rbrace $.

The equivalence class $\displaystyle \left[ (a,b)\right] $ consists of all pairs of numbers $\displaystyle (c,d)$ such that $\displaystyle ad=bc$, meaning $\displaystyle \left[ (a,b) \right]= \left\lbrace (c,d) \mid ad=bc \right\rbrace $.

Get back 2 me

Peace out