Show that for a set the sums of elements in the subsets of can produce any element of the set .
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Originally Posted by usagi_killer Show that for a set the sums of elements in the subsets of can produce any element of the set . For n= 1 (and for n= 2,3 also) the result is easily checked, so assume the result is true for k up to n-1 and prove for k = n. Now, let : 1) If then apply the inductive hypothesis to the subset , otherwise; 2) , and then it's easy to see that , with Tonio
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