{"id":1315,"date":"2017-07-06T09:33:22","date_gmt":"2017-07-06T01:33:22","guid":{"rendered":"http:\/\/www.xuehelp.cn\/?p=1315"},"modified":"2017-07-06T09:33:22","modified_gmt":"2017-07-06T01:33:22","slug":"%e7%8b%ac%e7%ab%8b%e6%80%a7%e8%af%81%e6%98%8e%e7%9a%84%e6%9c%89%e8%b6%a3%e6%95%85%e4%ba%8b","status":"publish","type":"post","link":"http:\/\/www.xuehelp.cn\/index.php\/archives\/1315","title":{"rendered":"\u72ec\u7acb\u6027\u8bc1\u660e\u7684\u6709\u8da3\u6545\u4e8b"},"content":{"rendered":"

\u5e02\u91cc\u53d1\u751f\u4e00\u8d77\u51f6\u6740\u6848\uff0c\u8b66\u65b9\u65ad\u5b9a\uff1a<\/p>\n

    \n
  1. \u51f6\u624b\u662f\u7537\u6027<\/li>\n
  2. \u53d7\u5bb3\u8005\u662f\u5973\u6027<\/li>\n
  3. \u51f6\u624b\u505a\u6848\u4e4b\u524d\u6709\u5927\u91cf\u996e\u9152<\/li>\n
  4. \u51f6\u624b\u7528\u53cc\u624b\u6390\u6b7b\u4e86\u53d7\u5bb3\u8005<\/li>\n<\/ol>\n

    <\/p>\n

    \u53d7\u5bb3\u8005\u7684\u4e08\u592b\u5728\u6848\u53d1\u73b0\u524d\u548c\u53d7\u5bb3\u8005\u6709\u8fc7\u6fc0\u70c8\u4e89\u5435\uff0c\u5e76\u4e14\u6848\u53d1\u65f6\u5c31\u5728\u6848\u53d1\u73b0\u573a\u9644\u8fd1\u3002\u7531\u4e8e\u662f\u5065\u7f8e\u6559\u7ec3\uff0c\u6709\u8db3\u591f\u7684\u624b\u529b\u6390\u6b7b\u4e00\u540d\u6210\u5e74\u5973\u751f\u3002\u5e76\u4e14\uff0c\u6709\u5f88\u591a\u6848\u4ef6\uff0c\u5728\u592b\u59bb\u53d1\u751f\u6fc0\u70c8\u51b2\u7a81\u540e\u53d1\u751f\u7684\u3002\u4e8e\u662f\u88ab\u63a7\u65b9\u9501\u5b9a\u4e3a\u91cd\u5927\u5acc\u7591\u4eba\u3002<\/p>\n

    \u53d7\u5bb3\u8005\u7684\u4e08\u592b\u7684\u5f8b\u5e08\u5374\u8bf4\uff1a\u53e6\u5916\u4e00\u4e2a\u57ce\u5e02\uff0c\u4e5f\u662f\u76f8\u540c\u60c5\u51b5\uff0c\u4f46\u53d7\u5bb3\u4eba\u662f\u88ab\u4e00\u4e2a\u6d41\u7a9c\u4f5c\u6848\u7684\u6d41\u52a8\u4eba\u5458\u6740\u5bb3\u7684\uff0c\u6240\u4ee5\u73b0\u6709\u8bc1\u636e\u65e0\u6cd5\u8bc1\u660e\u5acc\u7591\u4eba\u5c31\u662f\u51f6\u624b\u3002<\/p>\n

    \u5f53\u7136\uff0c\u76ee\u524d\u4e3a\u6b62\uff0c\u4e5f\u65e0\u6cd5\u8bc1\u660e\u5acc\u7591\u4eba\u662f\u51f6\u624b\u3002<\/p>\n

    \u6240\u4ee5\uff0c\u63a7\u8fa9\u53cc\u65b9\u90fd\u8981\u7ee7\u7eed\u627e\u8bc1\u636e\uff0c\u6765\u8bc1\u660e\u4ed6\u4eec\u76f8\u8981\u7684\u7ed3\u679c\u3002<\/p>\n

    \u5176\u5b9e\uff0c\u6570\u5b66\u516c\u7406\u5c31\u662f\u201c\u8bc1\u636e\u201d\u3002\u8fd9\u79cd\u201c\u8bc1\u636e\u201d\u662f\u4e00\u4e2a\u8981\u6c42\u4eba\u4eec\u5148\u63a5\u53d7\uff0c\u800c\u65e0\u9700\u8bc1\u660e\u7684\u4e00\u4e9b\u547d\u9898\u3002\u81f3\u4e8e\uff0c\u4e3a\u4ec0\u4e48\u8981\u63a5\u53d7\uff0c\u6216\u662f\u56e0\u4e3a\u751f\u6d3b\u7ecf\u9a8c\uff0c\u6216\u662f\u56e0\u4e3a\u67d0\u4e9b\u5b9e\u9a8c\u7ed3\u679c\uff0c\u518d\u6216\u6ca1\u6709\u4efb\u4f55\u7406\u7531\uff0c\u53cd\u6b63\u5148\u63a5\u53d7\u3002\u4f46\u63a5\u53d7\u7684\u4e1c\u897f\u4e4b\u95f4\u4e0d\u80fd\u6709\u77db\u76fe\u7684\u5730\u65b9\u3002\u6bd4\u5982\uff0c\u4e0b\u9762\u4e00\u4e32\u7684\u4e1c\u897f\uff0c\u4e0d\u80fd\u770b\u6210\u516c\u7406\u3002<\/p>\n

      \n
    1. \u4e16\u754c\u4e2d\u5b58\u5728\u4e24\u4e2a\u4eba\u7c7b\u5c0f\u660e\u548c\u5c0f\u7ea2<\/li>\n
    2. \u5c0f\u660e\u662f\u7537\u4eba<\/li>\n
    3. \u5c0f\u7ea2\u662f\u5973\u4eba<\/li>\n
    4. \u5c0f\u660e\u4e0e\u5c0f\u7ea2\u662f\u76f8\u540c\u6027\u522b\u7684<\/li>\n
    5. \u7537\u5973\u662f\u4e24\u4e2a\u4e0d\u540c\u6027\u522b<\/li>\n<\/ol>\n

      \u6211\u4eec\u518d\u6765\u8bf4\u4e00\u4e2a\u6570\u5b66\u7684\u4f8b\u5b50\uff0c\u9ad8\u7b49\u4ee3\u6570\u4e2d\u5b66\u8fc7\u6570\u57df\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u628a\u8fd9\u4e9b\u5b9a\u4e49\u7684\u6761\u4ef6\u770b\u6210\u516c\u7406\u5427\u3002\u4e00\u4e2a\u5b9e\u6570\u5b50\u96c6F<\/span><\/span><\/span>F<\/span><\/span>\uff0c\u6ee1\u8db3\u5c31\u662f\u4e0b\u9762\u51e0\u6761\u516c\u7406\uff0c\u5c31\u79f0\u4e3a\u6570\u57df(\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u53ea\u5728\u5b9e\u6570\u4e0a\u8ba8\u8bba)\u3002<\/p>\n

        \n
      1. 1<\/span>\u2208<\/span>F<\/span><\/span><\/span>1\u2208F<\/span><\/span><\/li>\n
      2. \u5982\u679ca<\/span>,<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a,b\u2208F<\/span><\/span>\uff0c\u5219a<\/span>+<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a+b\u2208F<\/span><\/span><\/li>\n
      3. \u5982\u679ca<\/span>,<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a,b\u2208F<\/span><\/span>\uff0c\u5219a<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>ab\u2208F<\/span><\/span><\/li>\n
      4. \u5982\u679ca<\/span>,<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a,b\u2208F<\/span><\/span>\uff0c\u5219a<\/span>\u2212<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a\u2212b\u2208F<\/span><\/span><\/li>\n
      5. \u5982\u679ca<\/span>,<\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a,b\u2208F<\/span><\/span>\uff0cb<\/span>\u2260<\/span>0<\/span><\/span><\/span>b\u22600<\/span><\/span>\uff0c\u5219a<\/span>\/<\/span><\/span><\/span>b<\/span>\u2208<\/span>F<\/span><\/span><\/span>a\/b\u2208F<\/span><\/span><\/li>\n<\/ol>\n

        \u90a3\u4e48\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6570\u57dfF<\/span><\/span><\/span>F<\/span><\/span>\uff0c\u7531\u8fd9\u51e0\u6761\u516c\u7406(\u52a0\u4e0a\u9ed8\u8ba4\u7684\u4e00\u4e9b\u516c\u7406\uff0c\u6bd4\u5982\u5b9e\u6570\u5b8c\u5907\u6027\u7684\u516c\u7406)\uff0c\u662f\u5426\u80fd\u63a8\u5bfc\u51fax<\/span>2<\/span><\/span>=<\/span>2<\/span><\/span><\/span>x2=2<\/span><\/span>\u5728F<\/span><\/span><\/span>F<\/span><\/span>\u4e0a\u6709\u89e3\uff1f\u6211\u4eec\u8bf4\uff0c\u4e0d\u80fd\uff0c\u56e0\u4e3a\u5982\u679c\u6211\u4eec\u8ba9F<\/span><\/span><\/span>F<\/span><\/span>\u4e3a\u6709\u7406\u6570\u96c6\u7684\u65f6\u5019\uff0c\u6709\u7406\u6570\u96c6\u662f\u4e00\u4e2a\u6570\u57df\uff0c\u4f46x<\/span>2<\/span><\/span>=<\/span>2<\/span><\/span><\/span>x2=2<\/span><\/span>\u65e0\u89e3\u3002\u90a3\u80fd\u5426\u63a8\u51fax<\/span>\u00b2<\/span><\/span><\/span>=<\/span>2<\/span><\/span><\/span>x\u00b2=2<\/span><\/span>\u65e0\u89e3\u5462\uff0c\u6211\u4eec\u8bf4\u4e5f\u4e0d\u80fd\uff0c\u56e0\u4e3a\u5982\u679c\u6211\u4eec\u8ba9F<\/span>=<\/span>R<\/span><\/span><\/span>F=R<\/span><\/span>\u65f6\uff0c\u5728\u8fd9\u4e2a\u57df\u4e0a\u662f\u6709\u89e3\u7684\u3002<\/p>\n

        \u4e8e\u662f\uff0c\u5f97\u5230\u7ed3\u8bba\u201c\u4ee3\u6570\u65b9\u7a0bx<\/span>2<\/span><\/span>=<\/span>2<\/span><\/span><\/span>x2=2<\/span><\/span>\u6709\u89e3\u201d\u8fd9\u4e2a\u547d\u9898\uff0c\u5728\u6570\u57df\u516c\u7406\u4f53\u7cfb\u4e0b\uff0c\u662f\u65e0\u6cd5\u8bc1\u660e\uff0c\u4e5f\u65e0\u6cd5\u8bc1\u4f2a\u7684\u3002\u4e8e\u662f\u8fd9\u4e2ax<\/span>2<\/span><\/span>=<\/span>2<\/span><\/span><\/span>x2=2<\/span><\/span>\u662f\u5426\u6709\u89e3\uff0c\u4e0e\u6570\u57df\u516c\u7406\u72ec\u7acb\u3002<\/p>\n

        \u901a\u8fc7\u4e0a\u9762\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u6211\u4eec\u8981\u4e00\u4e2a\u547d\u9898\u7684\u8bc1\u660e\u72ec\u7acb\u6027\uff0c\u6709\u4e00\u4e2a\u529e\u6cd5\u662f\uff0c\u627e\u4e24\u4e2a\u6a21\u578b\uff0c\u4e24\u4e2a\u6a21\u578b\u90fd\u6ee1\u8db3\u6240\u6709\u516c\u7406\u7684\u6761\u4ef6\uff0c\u4f46\u8fd9\u4e2a\u547d\u9898\u5728\u5176\u4e2d\u4e00\u4e2a\u6a21\u578b\u91cc\u662f\u771f\u547d\u9898\uff0c\u5728\u53e6\u5916\u4e00\u4e2a\u662f\u5047\u547d\u9898\uff08\u6bd4\u5982\u524d\u6587\u4e2d\u7684\u6709\u7406\u6570\u96c6\u548cR<\/span><\/span><\/span>R<\/span><\/span>\uff09\u3002<\/p>\n

        \u6211\u4eec\u90fd\u719f\u77e5\u7684\u8fde\u7eed\u7edf\u5047\u8bbe\u4e0eZFC\u516c\u7406\u7cfb\u7edf\u72ec\u7acb\u5c31\u662f\u7528\u8fd9\u6837\u7684\u529e\u6cd5\u8bc1\u660e\u7684\u3002<\/p>\n

        \u7b2c\u4e00\u4e2a\u627e\u5230\u8ba9\u8fde\u7eed\u7edf\u5047\u8bbe\u662f\u771f\u547d\u9898\u6a21\u578b\u662f\u54e5\u5fb7\u5c14\uff0c\u4ed6\u5229\u7528\u4e86\u6784\u9020\u6027\u516c\u7406\u3002\u7531\u4e8eZF\u548c\u6784\u9020\u6027\u516c\u7406\u4e00\u8d77\u8fd8\u80fd\u987a\u4fbf\u63a8\u51fa\u9009\u62e9\u516c\u7406\uff0c\u4e8e\u662f\u4ed6\u8bc1\u660e\u4e86\u8fde\u7eed\u7edf\u5047\u8bbe\u548cZFC\u662f\u4e0d\u77db\u76fe\u7684\u3002<\/p>\n

        \u627e\u5230\u53e6\u4e00\u4e2a\u8ba9\u8fde\u7eed\u7edf\u5047\u8bbe\u662f\u5047\u547d\u9898\u6a21\u578b\uff0c\u8981\u96be\u5f97\u591a\u3002\u4e0d\u8fc7\u8fd8\u662f\u7531\u79d1\u6069(P.J Cohen)\u627e\u5230\u4e86\uff0c\u627e\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4ed6\u7528\u4e86\u4ed6\u672c\u4eba\u53d1\u660e\u7684\u6570\u5b66\u5de5\u5177\u529b\u8feb\u6cd5(Forcing)\u3002\u4e8e\u662f\uff0c\u8fde\u7eed\u7edf\u5047\u8bbe\u4e0eZFC\u516c\u7406\u4f53\u7cfb\u5c31\u72ec\u7acb\u4e86\u3002\u7531\u6b64\uff0c\u79d1\u6069\u83b7\u5f97\u4e861966\u5e74\u7684\u83f2\u5c14\u5179\u5956\uff0c\u4e5f\u662f\u552f\u4e00\u4e00\u4e2a\u5728\u6570\u7406\u903b\u8f91\u9886\u57df\u7684\u83f2\u5c14\u5179\u5956\u7684\u83b7\u5f97\u8005\u3002<\/p>\n

        \u6700\u540e\u8865\u5145\u4e00\u70b9\uff0c\u6211\u4eec\u8bf4\u516c\u7406\u5c31\u662f\u201c\u8bc1\u636e\u201d\u3002\u73b0\u4ee3\u7684\u516c\u7406\u4ee3\u6570\u5b66\u5230\u5e95\u662f\u54ea\u4e9b\u201c\u8bc1\u636e\u201d\u5462\u3002\u8fd9\u4e9b\u8bc1\u636e\u88ab\u79f0\u4e3aZF\u516c\u7406\u4f53\u7cfb\u3002\u6211\u8fd9\u91cc\u5217\u4e3e\u4e00\u4e0b\uff0c\u4e0d\u8fc7\u6211\u5168\u90e8\u7528\u53e3\u8bed\u4e0d\u4e25\u8c28\u7684\u5217\u4e3e(\u4e25\u8c28\u7684\u8981\u7528\u5f62\u5f0f\u8bed\u8a00)\u3002<\/p>\n

          \n
        1. \u516c\u74061 \u5916\u5ef6\u516c\u7406
          \n\u4e24\u4e2a\u96c6\u5408\u6709\u76f8\u540c\u7684\u5143\u7d20\u5219\u4e24\u96c6\u5408\u76f8\u7b49<\/li>\n
        2. \u516c\u74062 \u6b63\u89c4\u516c\u7406
          \n\u6bcf\u4e2a\u975e\u7a7a\u96c6\u5408x<\/span><\/span><\/span>x<\/span><\/span> \u90fd\u5305\u542b\u4e00\u4e2a\u5143\u7d20y<\/span>\u2208<\/span>x<\/span><\/span><\/span>y\u2208x<\/span><\/span> \uff0c\u4f7f\u5f97x<\/span><\/span><\/span>x<\/span><\/span>\u548cy<\/span><\/span><\/span>y<\/span><\/span>\u4e0d\u76f8\u4ea4\u3002<\/li>\n
        3. \u516c\u74063 \u5206\u7c7b\u516c\u7406
          \nx<\/span><\/span><\/span>x<\/span><\/span>\u662f\u4e00\u4e2a\u96c6\u5408\uff0cp<\/span><\/span><\/span>p<\/span><\/span>\u662f\u4e00\u4e2a\u63cf\u8ff0\u96c6\u5408\u7684\u6027\u8d28\uff0c\u5219{<\/span>y<\/span>\u2208<\/span>x<\/span>:<\/span>\u00a0<\/span>p<\/span>(<\/span>y<\/span>)<\/span>}<\/span><\/span><\/span>{y\u2208x:\u00a0p(y)}<\/span><\/span>\u662f\u4e00\u4e2a\u96c6\u5408<\/li>\n
        4. \u516c\u74064 \u914d\u5bf9\u516c\u7406
          \nx<\/span>,<\/span>y<\/span><\/span><\/span>x,y<\/span><\/span>\u90fd\u662f\u96c6\u5408\uff0c\u5219{<\/span>x<\/span>,<\/span>y<\/span>}<\/span><\/span><\/span>{x,y}<\/span><\/span>\u4e5f\u662f\u96c6\u5408\u3002<\/li>\n
        5. \u516c\u74065 \u5e76\u96c6\u516c\u7406
          \n\u4e00\u7c07\u96c6\u5408\u7684\u5e76\uff0c\u8fd8\u662f\u96c6\u5408\u3002<\/li>\n
        6. \u516c\u74066 \u66ff\u4ee3\u516c\u7406\u6a21\u5f0f
          \n\u4e00\u4e2a\u96c6\u5408\u88ab\u6620\u5c04\u540e\uff0c\u5f97\u5230\u5230\u7684\u50cf\u8fd8\u662f\u4e00\u4e2a\u96c6\u5408\u3002\u8fd9\u4e2a\u516c\u7406\u4e4b\u6240\u4ee5\u79f0\u4e3a\u6a21\u5f0f\uff0c\u65e0\u7a77\u591a\u7684\u6620\u5c04\uff0c\u5bf9\u540c\u4e00\u4e2a\u96c6\u548c\u90fd\u80fd\u4ea7\u751f\u50cf\uff0c\u8fd9\u4e9b\u50cf\u90fd\u662f\u96c6\u5408\u3002\u6240\u4ee5\u8fd9\u5176\u5b9e\u65e0\u7a77\u591a\u6761\u516c\u7406\u3002<\/li>\n
        7. \u516c\u74067 \u65e0\u7a77\u516c\u7406
          \n\u5b58\u5728\u4e00\u4e2a\u65e0\u9650\u4e2a\u5143\u7d20\u7684\u96c6\u5408(\u6240\u6709\u81ea\u7136\u6570\u5728\u4e00\u8d77\u662f\u96c6\u5408)\u3002<\/li>\n
        8. \u516c\u74068 \u5e42\u96c6\u516c\u7406
          \n\u4e00\u4e2a\u96c6\u5408\u7684\u5b50\u96c6\u505a\u5143\u7d20\uff0c\u80fd\u5f62\u6210\u4e00\u4e2a\u96c6\u5408\u3002<\/li>\n<\/ol>\n

          \u4e0a\u97628\u6761\u5c31\u6784\u6210ZF\u516c\u7406\u4f53\u7cfb\uff0c\u518d\u52a0\u4e0a\u4e0b\u9762\u7684\u9009\u62e9\u516c\u7406\uff0c\u5c31\u662fZFC\u516c\u7406\u4f53\u7cfb\u3002<\/p>\n

            \n
          1. \u516c\u74069 \u9009\u62e9\u516c\u7406
            \n\u5bf9\u4e00\u7c07\u96c6\u5408\uff0c\u6211\u4eec\u53ef\u4ee5\u6bcf\u4e00\u4e2a\u96c6\u5408\u91cc\u6293\u51fa\u4e00\u4e2a\u6765\uff0c\u5f62\u6210\u4e00\u4e2a\u65b0\u96c6\u5408\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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