Suppose \(v \in V\), and \(U \subset V\). Then, \(v+U\) is the *subset* (not a subspace, obviously):

\begin{equation} v + U = \{v+u : u \in U\} \end{equation}

Suppose \(v \in V\), and \(U \subset V\). Then, \(v+U\) is the *subset* (not a subspace, obviously):

\begin{equation} v + U = \{v+u : u \in U\} \end{equation}