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Say we have sets $X = \{0,2,3\}$ and $Y = \{1,2,5\}$.
Is the sumset defined to be
$X + Y = \{0 + 1,2 +2,3+5\} = \{1,4,8\}$
or summing every element pairwise
$X + Y = \{1,2,5,3,4,7,8\} $
?
1 Answer
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$$ A + B = \{a+b : a \in A, b \in B\}. $$ If $X = \{0,2,3\}$ and $Y = \{1,2,5\}$. $$X+Y=\{0+1;0+2;0+5;2+1;2+2;2+5;3+1;3+2;3+5\}$$
