Suppose $A\subset\{0,1\}^d$ for some $d\geq 1$. Then how large must $A+A=\{a+b:a,b\in A\}$ be?
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5$\begingroup$ $|A+A|$ can be as small as $0$ (if $A=\emptyset$), and $|A+A|/|A|$ can be as small as $1$ (if $A$ is a singleton). You should be more specific with your question! $\endgroup$– SevaCommented Feb 25, 2017 at 16:32
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3$\begingroup$ You might also want to clarify if addition is in $\mathbb Z$ or $\mathbb F_2$. $\endgroup$– Brendan McKayCommented Feb 26, 2017 at 4:46
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