# Thread: Isomorphism between R/R and {0}

1. ## Isomorphism between R/R and {0}

if R is a ring, why is there an isomorphism between R/R and {0}?
I don't understand how is it even possible because R/R = R.
Thanks.

2. $[x],[y]\in R/R$

are equal iff

$x-y\in R$

This happen for all $x,y\in R$ so, $R/R$ has only one element:

$R/R=\{[0]\}$

Fernando Revilla