= Superincreasing sequence
{title2=$w_k>\sum_{j<k}w_j$}
A positive sequence is superincreasing if each term exceeds the sum of all earlier terms. If $w_{k+1}>2w_k$, a <geometric series> proves $\sum_{j<k}w_j<w_k$. Distinct finite subsets of its indices have distinct sums: cancel their common terms and compare the largest remaining term with the sum of all smaller terms. This gives uniqueness of <minimum spanning trees> and of simple <graph paths> with fixed endpoints when a finite <weighted graph> has such separated edge weights.
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