If $S$ is a subset, is $S+\emptyset$ defined and equals to $S$? Or is it just gibberish? Thanks again.
Validity of the notation $S+\emptyset$
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linear-algebra
notation
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2Assuming 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