Suppose $U$ is a subspace of $V$. It seems that any element in $\{u+U:u\in U\}$ could be the additive identity of the quotient space $V/U$. And for any $v+U \in V/U$, any element in $\{(-v+u)+U:u\in U\}$ could be its additive inverse. Does that mean additive identity and additive inverse might not be unique?
2026-03-29 03:35:42.1774755342
Are the additive identity and additive inverse of a quotient space unique?
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