sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence.

Thanks Sundi

closed as off-topic by Ricardo Andrade, Evan Jenkins, Steven Landsburg, Andrés E. Caicedo, Andrey RekaloOct 19 '13 at 7:39

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• The sequence $.1, .01, .001, .0001,\ldots$ will do the trick. – Barry Cipra May 9 '13 at 13:53

Other sequences that immediately come to mind are vector-like expressions $$(1, 0, 0, 0, 0, ...), (0, 1, 0, 0, 0, ...) , (0, 0, 1, 0, 0, ...), ...$$ (or matrices or tensors) or the sequence $(a_n)$ of approximations of transcendentals like Liouville's number $$a_n = \sum_{k=0}^{n} \frac{1}{k!}$$ or just terminating rationals with different points of termination behind the decimal point $$0.1, 0.11, 0.111, ...$$ or before$$1, 10, 100, ...$$