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I sometimes see this notation for convergence (speaking for functions): $f_n \to f$. And sometimes, I see following: $f_n \nearrow f$ or $f_n \searrow f$. What is the difference between $\to$ and other two?

Thanks.

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    Please, try to make the title of your question more informative. E.g., *Why does $a imply $a+c?* is much more useful for other users than *A question about inequality.* From [How can I ask a good question?](http://meta.math.stackexchange.com/a/589/): *Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader.*2012-11-12
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    @JulianKuelshammer thanks. It was hard to embed all information to the header, but I tried. I hope it is OK. Thanks.2012-11-12
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    Now it's perfect.2012-11-12

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The first generally means that the sequence of functions is pointwise non-decreasing, the second that it’s pointwise non-increasing. Sometimes a strict ordering is meant instead, so that the sequences are pointwise strictly increasing and pointwise strictly decreasing, respectively.

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    OK, then $\to$ can mean one of these $\nearrow$ or $\searrow$?2012-11-12
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    @John: Yes, but $\to$ also covers non-monotonic convergence.2012-11-12
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    Brian: now I got it. Thanks!2012-11-12
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    @John: You’re welcome!2012-11-12