0
$\begingroup$

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

Improve this question
$\endgroup$
1
  • $\begingroup$ The sequence $.1, .01, .001, .0001,\ldots$ will do the trick. $\endgroup$
    – Barry Cipra
    Commented May 9, 2013 at 13:53

2 Answers 2

Reset to default
1
$\begingroup$

got it, thanks, just a gp series would do. 1,2,4,8,16...

Improve this answer
$\endgroup$
1
$\begingroup$

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

But that's already very close to the first answer.

Improve this answer
$\endgroup$
0

Not the answer you're looking for? Browse other questions tagged .