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If $S$ is a subset, is $S+\emptyset$ defined and equals to $S$? Or is it just gibberish? Thanks again. 

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    Assuming that $A+B = \{ a + b \,:\, a \in A, b \in B \}$, we have $S + \{ \mathbf 0 \} = S$ and $S + \emptyset = \emptyset$. ($\mathbf 0$ is the additive identity, aka the zero vector.)2011-09-10

2 Answers 2