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?
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.