# 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

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

## closed as off-topic by Ricardo Andrade, Evan Jenkins, Steven Landsburg, Andres Caicedo, Andrey RekaloOct 19 at 7:39

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Ricardo Andrade, Evan Jenkins, Steven Landsburg, Andres Caicedo, Andrey Rekalo
If this question can be reworded to fit the rules in the help center, please edit the question.

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$$1, 10, 100, ...$$