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<div>:: <span class="kw">deftheorem </span>   defines <a href="dblseq_3.html#V1" title="DBLSEQ_3:attr.1">P-convergent_to_finite_number</a> <a onclick="hs(this)" href="javascript:()">DBLSEQ_3:def 1 : <br/></a><span> for <font color="Olive" title="b1">Eseq</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> ( <font color="Olive" title="b1">Eseq</font> is  <a href="dblseq_3.html#V1" title="DBLSEQ_3:attr.1">P-convergent_to_finite_number</a>  iff  ex <font color="Olive" title="b2">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/> for <font color="Olive" title="b3">e</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">e</font> holds <br/> ex <font color="Olive" title="b4">N</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/> for <font color="Olive" title="b5">n</font>, <font color="Olive" title="b6">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b4">N</font> &amp; <font color="Olive" title="b6">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b4">N</font> holds <br/><span class="p1"><a href="extreal1.html#K3" title="EXTREAL1:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">Eseq</font> <a href="dblseq_3.html#K6" title="DBLSEQ_3:func.6">.</a> (<font color="Olive" title="b5">n</font>,<font color="Olive" title="b6">m</font>)</span>)</span> <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <font color="Olive" title="b2">p</font></span>)</span></span><a href="extreal1.html#K3" title="EXTREAL1:func.3">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">e</font> );<br/></span></div>
