If " X " is a Hausdorff space then limits of sequences are unique where they exist.
2.
As in the case of limits of sequences, least upper bounds of directed sets do not always exist.
3.
In fact, a function " f " is continuous if and only if it preserves the limits of sequences.
4.
The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes.
5.
However, Riemann integration does not interact well with taking limits of sequences of functions, making such limiting processes difficult to analyze.
6.
Then a limiting procedure allows assigning probabilities to sets that are limits of sequences of generator sets, or limits of limits, and so on.
7.
*PM : limit of sequence as sum of series, id = 9858 new !-- WP guess : limit of sequence as sum of series-- Status:
8.
*PM : limit of sequence as sum of series, id = 9858 new !-- WP guess : limit of sequence as sum of series-- Status:
9.
In an alternative and more general definition of weakly simple polygons, they are the limits of sequences of simple polygons of the same combinatorial type, with the convergence under the Fr�chet distance.
10.
In fact, any real-valued function " f " is continuous if and only if it preserves the limits of sequences ( though this is not necessarily true when using more general notions of continuity ).
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