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<p> there is a positive <a href="page.php?w=integer">integer</a>  such that for all positive integers   </p>

<p><b>Complete space</b></p>

<p>A metric space  is <b>complete</b> if any of the following equivalent conditions are satisfied:<br/>
#Every Cauchy sequence in  converges in  (that is, has a limit that is also in ).<br/>
#Every decreasing sequence of <a href="page.php?w=empty_set">non-empty</a> <a href="page.php?w=closed_subset">closed subset</a>s of  with <a href="page.php?w=Diameter_of_a_set">diameters</a> tending to&nbsp;0, has a non-empty</p><p>
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