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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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    Your name on this site is weird, considering the nature of your question.2012-12-05
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    Is the symbol Φ really correct? From the context, I'd think that notation should be a "not equals" sign, which your copy-paste process has misread as a capital Phi.2012-12-05
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    @KCd Thanks, you are right. I have revised the question.2012-12-05
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    I am curious: how is it that you need a translation of *just this part*, and not some whole page or section containing it?2012-12-05
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    @KCd Because this question instead of others is a homework.2012-12-05
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    This is homework for a math class? It doesn't make any sense as a homework problem, since it looks like two consecutive sentences randomly pulled out of a book.2012-12-05
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    @KCd last week's lesson I have learned the definition of "independence of sequences system". That is, two or more sequences $\{a^{(s)}\}$ satisified $k_1a^{(1)}+k_2a^{(2)}+\dots+k_sa^{(s)}=0$ only when the $k_i=0$, $i=1$ to $s$. The class is craming.2012-12-05
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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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    It'd be better to say "essentially different" instead of "significantly different".2012-12-05
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    @Sasha Thanks. The $\Phi$ is a typo. You can see the edited post.2012-12-05
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    @Sasha Could you give an example for the subsequences?2012-12-05
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    @KCd Thanks for the suggestion. I have updated the text accordingly.2012-12-05
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    Sasha: the text needs updating in two parts, since существенно различная shows up twice.2012-12-05
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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