YLL討論網

由 **linch6123** 於星期四四月 06, 2006 1:22 am

#ed_op#DIV#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"#ed_cl#因為#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-FAMILY: Verdana"#ed_cl#{x#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}be a cauchy sequence in a metric space X . #ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#且#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-FAMILY: Verdana"#ed_cl# {x#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}has a convergent subsequence in X#ed_op#?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /#ed_cl##ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl##ed_op#/SPAN#ed_cl# #ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; 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mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#＝#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-FAMILY: Verdana"#ed_cl# #ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#ε#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-FAMILY: Verdana"#ed_cl##ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN lang=EN-US style="FONT-FAMILY: Verdana"#ed_cl##ed_op#o:p#ed_cl# #ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#這題我沒啥把握#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-FAMILY: Verdana"#ed_cl##ed_op#SPAN style="mso-spacerun: yes"#ed_cl#  有問題再一起討論#ed_op#/SPAN#ed_cl##ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

由 **cloudsea** 於星期三四月 05, 2006 8:05 am

#ed_op#DIV#ed_cl#Let {x#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}be a cauchy sequence in a metric space X .  Suppose {x#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}has a convergent subsequence in X .Prove or disprove {x#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}itself converges in X.#ed_op#/DIV#ed_cl#

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