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Math Help - limit superior ....

  1. #1
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    limit superior ....

    Find   \overline{lim} \ a_n where :
     a_n = \begin{cases}<br />
1 &,  \text{ if } n\ is \ square \\ <br />
0 &, \text{ if } n \ not \ square  <br />
\end{cases}
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by flower3 View Post
    Find   \overline{lim} \ a_n where :
     a_n = \begin{cases}<br />
1 &,  \text{ if } n\ is \ square \\ <br />
0 &, \text{ if } n \ not \ square  <br />
\end{cases}
    Let S represent the set of all subsequential limits of a_n. Evidently S=\{0,1\} and so \limsup\text{ }a_n=\sup\text{ }S=1
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