Why quotient ring $R/R$ is zero ring $\{ 0\}$? There is already similar question.
Factor rings $R/R$ and $R/0$
Of course, I read it. However I still don't know, how and why the quotient ring $R/R$ is zero ring. So, I ask your help to check my thinking logic.

In my opinion, it seems to be $R/R=R$.
The definition of the quotient ring is $R/P=\{r+P|r \in R\}$.
So, $R/R=\{r+R|r \in R\}$. Does $r+R$ make all of element of $R$?
And if $R$ is a commutative ring with identity, is that something different result?

I think I have a big problem with that logic, but I'm blind to find it. 
I hope your brighter sight.
Thank you in advance.

See the first thing you should understand is the following: 
$$ R/P:= \text{Set of equivalence classes where the relation is defined as $r\sim s\iff (r-s)\in P$}   $$
Now, what will be $R/R$? It is the set of equivalence classes of the above relation. Now we claim that there is only one class and that class will be $[0]$ class. The intuitive answer is given in the problem that you linked. But if you wanted to be more precise just show the following:
$R/R=\{[0]\}$. 
Let $[r]=r+R\in R/R. \ [r]= r+R=0+(r+R)=[0] \implies R/R\subseteqq \{[0]\}.$ The other inclusion is trivial. 
