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I found it in the section of sequence space.

Две последовательности $\{a_n\}$ и $\{b_n\}$ называем существенно различными, если $a_n\ne b_n$ для бесконечного множества натуральных чисел. Каждая конечная система существенно различных подпоследовательностей последовательности простых чисел образует линейно независимую систему.

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    There is no such thing as "independence of sequences system". You're looking for the term "linearly independent sequences". Anyway, I strongly recommend you understand what linearly independent vectors are in R^n before you try to come to grips with that concept in a space of sequences (where it's the same idea, but just a fancier setting).2012-12-05

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Here is the translation to the best of my understanding:

Two sequences $\{a_n\}$ and $\{b_n\}$ are called essentially different if $a_n \not= b_n$ for infinitely many natural numbers. Each finite system of essentially different subsequences of the sequence of prime numbers forms linearly independent system.

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    @Russianborme: if you can't figure out an example yourself even after seeing the translation into English, I think you should work harder yourself at trying to understand the concepts (i.e., think yourself about how two sequences could have $a_n \not= b_n$ for infinitely many $n$). You did say in a comment to your question that this is homework, after all.2012-12-05