I was given this question (there were prior questions defining the equivelence relation ~)
Let $E$ be the set of equivelence classes of $\sim$. Define $f$ from $E$ to $\mathbb R$, $$f:=\{([(x,y)],r)|x=yr,\: x,y,r\text{ in }\mathbb R\}.$$
I'm trying to understand what it means; is the following correct?
$f:[(x,y)] \mapsto r$,
$E=(\mathbb R \times {\mathbb R\setminus \{0\}})/\sim$: i.e. the Quotient set of $(\mathbb R\times (\mathbb R\setminus \{0\}))$ by $\sim$.
$(x,y)$ was earlier defined as an element of $(\mathbb R \times (\mathbb R\setminus\{0\})$.
Am I understanding this right?
My function takes in a equivlence class, $[(x,y)]$ and returns a real value $r$, fufilling the condition that $x=yr$?