I am reading Linear Algebra Done Right 3rd Edition.
Say, we have a subspace $U$ of vector space $V$. The book says that a quotient space is defined by $V/U = \{v + U: v \in U \}$
It then says that the additive identity of $V/U$ is $0+U$ and the additive inverse is $-v + U$. I didn't understand how the additive identity and additive inverse is that.