{"id":266,"date":"2008-03-19T23:12:59","date_gmt":"2008-03-19T15:12:59","guid":{"rendered":"http:\/\/home.wangjianshuo.com\/wordpresscn\/20080319_eceee_caee.htm"},"modified":"2008-03-19T23:12:59","modified_gmt":"2008-03-19T15:12:59","slug":"eceee_caee","status":"publish","type":"post","link":"https:\/\/home.wangjianshuo.com\/cn\/20080319_eceee_caee.htm","title":{"rendered":"\u5b8f\u89c2\u7684\u601d\u8003\u95ee\u9898 – \u7b2c\u4e8c\u90e8\u5206"},"content":{"rendered":"

\u524d\u51e0\u5929\u8d34\u4e86\u4e24\u4e2a\u6781\u9650\u76f8\u5173\u7684\u95ee\u9898<\/a>\u3002\u6211\u4ece\u8fd9\u79cd\u5947\u602a\u7684\u95ee\u9898\u91cc\u9762\u5b66\u5230\u7684\uff0c\u548c\u4ee5\u524d\u7684\u201c\u628a\u5927\u8c61\u653e\u8fdb\u51b0\u7bb1<\/a>\u201d\u7684\u95ee\u9898\u4e00\u6837\uff0c\u4e5f\u662f\u5173\u4e8e\u5b8f\u89c2\u548c\u5fae\u89c2\u7684\u533a\u522b\u3002\uff08\u6211\u5468\u56f4\u7684\u4eba\u5df2\u7ecf\u5feb\u88ab\u6211\u7684\u8fd9\u4e9b\u602a\u95ee\u9898\u7ed9\u903c\u75af\u4e86\uff09<\/p>\n

\u7b2c\u4e00\u4e2a\u95ee\u9898\uff1a<\/p>\n

0.9999\u2026.\u65e0\u9650\u5faa\u73af\u548c1\u90a3\u4e2a\u5927\uff1f<\/p><\/blockquote>\n

\u5b83\u4eec\u4e24\u4e2a\u6570\u5b66\u4e0a\u4e25\u683c\u76f8\u7b49\u3002\u8bc1\u660e\u65b9\u6cd5\u4e94\u82b1\u516b\u95e8\uff0c\u53ef\u4ee5\u5f00\u4e2a\u5c0f\u578b\u535a\u89c8\u4f1a\u3002\u6211\u5e38\u5e38\u91c7\u7528\u7684\u7b80\u5355\u65b9\u6cd5\u662f\uff1a<\/p>\n

\n1\/3 = 0.3333\u2026.
\n1\/3 * 3 = 0.333\u2026 * 3
\n1 = 0.999\u2026\n<\/p><\/blockquote>\n

\u6211\u559c\u6b22\u66f4\u52a0\u4e25\u8c28\u4e00\u70b9\u7684\u65b9\u6cd5\uff1a<\/p>\n

\nx = 0.999\u2026
\n10 x = 9.999\u2026
\n10 x = 9 + 0.999\u2026
\n10 x = 9 + x
\n9x = 9
\nx = 1
\n\u6240\u4ee5 0.999\u2026 = 1\n<\/p><\/blockquote>\n

\u8fd8\u6709\u5f88\u591a\u50cf\u524d\u9762\u7684\u8bc4\u8bba\u8005\u6240\u8bf4\u7684\uff0c\u627e\u4e0d\u51fa\u4efb\u4f55\u4e00\u4e2a\u6bd40.999\u2026\u5927\u4f46\u662f\u6bd41\u5c0f\u7684\u6570\uff0c\u6240\u4ee5\u4ed6\u4eec\u4e00\u6837\u5927\uff1b\u6216\u8005\u6309\u71670.999\u2026\u7b49\u4e8e\u5faa\u73af\u4f4d\u9664\u4ee59\u7684\u6807\u51c6\u7b97\u6cd5\uff0c\u4e5f\u5c31\u662f9\/9\u3002\u3002\u3002\u7b49\u7b49<\/p>\n

\u5176\u5b9e\u8fd9\u53ea\u662f\u4e00\u4e2a\u521d\u6b65\u7684\u6781\u9650\u95ee\u9898\uff0c\u771f\u6b63\u6bd4\u8f83\u9ebb\u70e6\u7684\u662f\u4e4c\u9f9f\u548c\u5154\u5b50\u7684\u95ee\u9898\u3002<\/p>\n

\u9f9f\u5154\u8d5b\u8dd1\uff0c\u5154\u5b50\u901f\u5ea6\u662f\u4e4c\u9f9f\u7684\u4e24\u500d\u3002\u4e4c\u9f9f\u6bd4\u5154\u5b50\u9886\u5148\u4e00\u7c73\uff0c\u4e00\u8d77\u8d77\u8dd1\uff0c\u5374\u6709\u79cd\u65b9\u6cd5\u53ef\u4ee5\u8bc1\u660e\u5154\u5b50\u6c38\u8fdc\u8ffd\u4e0d\u4e0a\u4e4c\u9f9f\uff1a<\/p>\n

\u5f53\u5154\u5b50\u5230\u4e86\u4e4c\u9f9f\u51fa\u53d1\u7684\u5730\u65b9\uff0c\u4e4c\u9f9f\u4f1a\u524d\u8fdb1\/2\u7c73\uff1b\u800c\u5f53\u5154\u5b50\u5230\u8fbe1\/2\u7c73\u7684\u65f6\u5019\uff0c\u4e4c\u9f9f\u53c8\u4f1a\u524d\u8fdb1\/4\u7c73\u3002\u3002\u3002\u3002\u603b\u4e4b\uff0c\u53ef\u4ee5\u8bc1\u660e\uff0c\u53ea\u8981\u5154\u5b50\u5230\u8fbe\u4e4c\u9f9f\u7684\u524d\u4e00\u4e2a\u65f6\u523b\u6240\u5728\u7684\u70b9\uff0c\u4e4c\u9f9f\u4e00\u5b9a\u4f1a\u524d\u8fdb\u521a\u624d\u8fc7\u53bb\u7684\u65f6\u95f4\u6bb5\u91cc\u9762\u5154\u5b50\u524d\u8fdb\u8ddd\u79bb\u76841\/2\u3002\u662f\u5426\u5154\u5b50\u6c38\u8fdc\u8ffd\u4e0d\u4e0a\u4e4c\u9f9f\u5462\uff1f\n<\/p><\/blockquote>\n

\u4ece\u5fae\u89c2\u770b\u6765\uff0c\u5154\u5b50\u8ffd\u4e4c\u9f9f\u7684\u6bcf\u4e00\u6b65\u90fd\u8ffd\u4e0d\u4e0a\u7684\u7ed3\u8bba\u90fd\u662f\u6210\u7acb\u7684\uff0c\u4e0d\u4ec5\u5982\u6b64\uff0c\u66f4\u8981\u547d\u7684\u662f\uff0c\u8fd9\u4e2a\u7b97\u5f0f\u8fd8\u662f\u65e0\u9650\u5faa\u73af\u7684\u3002\u597d\u4f3c\u65e0\u9650\u4e2a\u8ffd\u4e0d\u4e0a\uff0c\u7ed3\u679c\u5c31\u66f4\u52a0\u8ffd\u4e0d\u4e0a\u4e86\uff0c\u6216\u8005\u8bf4\uff0c\u65e0\u9650\u4e2a\u5c0f\u6570\u7684\u52a0\u548c\u771f\u7684\u6210\u4e86\u65e0\u9650\u5927\u4e00\u6837\u3002<\/p>\n

\u4f46\u5982\u679c\u6362\u4e2a\u89d2\u5ea6\u6765\u8bf4\uff0c\u4ece\u5b8f\u89c2\u770b\u8fd9\u4e2a\u95ee\u9898\uff0c\u5154\u5b50\u600e\u4e48\u53ef\u80fd\u8ffd\u4e0d\u4e0a\u4e4c\u9f9f\u5462\uff1f<\/p>\n

\u5982\u679c\u6211\u4eec\u770b\u4e00\u4e0b\u4e4c\u9f9f\u8dd1\u51fa\u53bb\u76841\/2 + 1\/4 + 1\/8 + \u2026.\u5230\u5e95\u6709\u591a\u8fdc\uff0c\u5c31\u604d\u7136\u5927\u609f\u4e86\u3002<\/p>\n

\nx = 1\/2 + 1\/4 + 1\/8 + \u2026
\n2 * x = 1 + ( 1\/2 + 1\/4 + 1\/8 + \u2026 )
\n2x = 1 + ( x )
\nx = 1
\n\u6240\u4ee5 1\/2 + 1\/4 + 1\/8 + .. = 1<\/p><\/blockquote>\n

\u4e5f\u5c31\u662f\uff0c\u65e0\u8bba\u4e4c\u9f9f\u6709\u591a\u5c11\u4e2a\u8fd9\u6837\u7684\u5c0f\u6b65\u5b50\uff0c\u6700\u7ec8\u4ed6\u8dd1\u51fa\u7684\u4e0d\u8fc71\u7c73\u3002\u4ece\u5b8f\u89c2\u4e0a\u770b\uff0c\u5154\u5b50\u5c06\u57281\u7c73\u5904\u5728\u6570\u5b66\u4e0a\u4e25\u683c\u7684\u548c\u4e4c\u9f9f\u5230\u8fbe\u540c\u4e00\u4e2a\u70b9\uff0c\u800c\u4e0d\u7ba1\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u6709\u591a\u5c11\u201c\u7ec6\u8282\u201d\u3002<\/p>\n

\u5173\u6ce8\u5fae\u89c2\u8fd8\u662f\u5b8f\u89c2<\/b><\/p>\n

\u6211\u4eec\u5e38\u8bf4\uff0c\u4ec0\u4e48\u4e8b\u60c5\u90fd\u662f\u79ef\u5c11\u6210\u591a\u3002\u4f46\u8fd9\u4e2a\u7b49\u5f0f\u8981\u770b\u5c0f\u7684\u5230\u5e95\u6709\u591a\u5c0f\u3002<\/p>\n

\u5728\u5fae\u89c2\u5c42\u9762\u6709\u5f88\u591a\u96be\u4ee5\u56de\u7b54\u7684\u95ee\u9898\uff0c\u96be\u505a\u5f97\u51b3\u5b9a\uff0c\u5728\u5b8f\u89c2\u4e0a\uff0c\u90fd\u53d8\u5f97\u7b80\u5355\u3002\u65e5\u5e38\u7684\u51b3\u5b9a\uff0c\u4ece\u5fae\u89c2\u4e0a\u770b\uff0c\u5728\u53d6\u820d\u4e4b\u95f4\u5f88\u96be\u5224\u65ad\uff0c\u65e0\u8bba\u5f80\u5de6\u8fd8\u662f\u5f80\u53f3\uff0c\u90fd\u4f1a\u5bf9\u9879\u76ee\u7684\u7ed3\u679c\u6709\u4e00\u4e9b\u5c0f\u7684\u5f71\u54cd\uff1b\u4f46\u662f\u5982\u679c\u9000\u51fa100\u7c73\u6765\u770b\uff0c\u5c31\u4f1a\u53d1\u73b0\uff0c\u5c31\u7b97\u6574\u4e2a\u9879\u76ee\u90fd\u4e0d\u505a\u4e86\uff0c\u5bf9\u4e8e\u5927\u5c40\u90fd\u6ca1\u6709\u4ec0\u4e48\u5f71\u54cd\uff0c\u53c8\u4e3a\u4ec0\u4e48\u56ff\u4e8e\u4e00\u4e2a\u53c8\u4e00\u4e2a\u7684\u7ec6\u8282\uff0c\u94bb\u8fdb\u725b\u89d2\u5c16\u5462\uff1f<\/p>\n

\u4eba\u7684\u8111\u5b50\u601d\u8003\u95ee\u9898\uff0c\u9664\u975e\u7ecf\u8fc7\u7279\u522b\u7684\u8bad\u7ec3\uff08\u5fae\u79ef\u5206\u662f\u8bad\u7ec3\u7684\u4e00\u79cd\uff09\uff0c\u90fd\u662f\u7ebf\u6027\u7684\u3002\u800c\u4e16\u754c\u7684\u6bd4\u4f8b\uff0c\u5c31\u50cf\u63d0\u51fa\u7684\u4e24\u4e2a\u6781\u9650\u95ee\u9898\u4e00\u6837\uff0c\u603b\u662f\u8ba9\u4eba\u65e0\u6cd5\u7406\u89e3\u3002\u6570\u5b66\u95ee\u9898\u5982\u662f\uff0c\u51b3\u7b56\u7684\u95ee\u9898\u5982\u662f\uff0c\u4eba\u751f\u7684\u95ee\u9898\u4e5f\u5982\u662f\u3002<\/p>\n

\u5bf9\u4e8e\u751f\u6d3b\uff0c\u6211\u4eec\u90fd\u77e5\u9053\u5b83\u662f\u7531\u4e00\u70b9\u4e00\u6ef4\u7684\u6784\u6210\u7684\u3002\u6ca1\u6709\u4e00\u4e2a\u4e00\u4e2a\u7684\u65f6\u95f4\u6bb5\uff0c\u5c31\u6ca1\u6709\u6708\uff0c\u5c31\u6ca1\u6709\u5e74\u3002\u4f46\u662f\u771f\u6b63\u91cd\u8981\u7684\u8fd8\u662f\u90a3\u4e9b\u5b8f\u89c2\u9898\uff1a2007\u5e74\u4f60\u5728\u5e72\u4e9b\u4ec0\u4e48\u5462\uff1f2006\u5e74\u5462\uff1f\u4ece\u5e74\u7684\u89d2\u5ea6\u770b\u95ee\u9898\uff0c\u5f88\u591a\u7684\u7ec6\u8282\u8fd8\u90a3\u4e48\u91cd\u8981\u5417\uff1f\u6216\u8bb8\u91cd\u8981\u7684\u662f\uff0c2007\u5e74\u4e00\u5e74\u5e72\u4e86\u4ec0\u4e48\uff0c\u800c\u4e0d\u662f\u54ea\u4e00\u79d2\u949f\u5e72\u4e86\u4ec0\u4e48\u5427\u3002<\/p>\n

\u6ce8\u4e00\uff1a\u5468\u4e00\uff0c\u6211\u548c\u6587\u5cf0\u5e86\u795d\u6211\u4eec\u7ed3\u5a5a\u4e94\u5468\u5e74\u3002\u5e78\u798f\u7684\u4e94\u5e74\uff0c\u8c22\u8c22\u6587\u5cf0\u7684\u966a\u4f34\u3002\u6211\u6700\u503c\u5f97\u9a84\u50b2\u7684\u5c31\u662f\u6211\u7684\u6587\u5cf0\u548c\u9038\u51e1\uff0c\u4ed6\u4eec\u8ba9\u6211\u7684\u6bcf\u4e00\u5206\u949f\u90fd\u5e78\u798f\u3002<\/p>\n

\u6ce8\u4e8c\uff1a\u8fd9\u5468\u6bcf\u5929\u665a\u4e0a7\u70b9\u534a\u52308\u70b9\uff0c\u4ee5\u53ca\u7b2c\u4e8c\u5929\u4e2d\u534812\u70b9\u534a\u5230\u4e00\u70b9\uff0c\u6211\u4f1a\u51fa\u73b0\u5728\u4e0a\u6d77\u7535\u89c6\u53f0\u56fd\u9645\u9891\u9053ICS\u7684\u300a\u8bf4\u4e1c\u9053\u897f\u300b\u8bbf\u8c08\u8282\u76ee\u30022000\u5e74\uff0c\u7b2c\u4e00\u6b21\u5728\u4e2d\u592e\u53f0\u7684\u4e00\u4e2a\u65b0\u95fb\u8282\u76ee\u7684\u4e00\u4e2a\u5c0f\u5c0f\u7684\u89d2\u843d\u9732\u4e86\u4e00\u5f20\u5c0f\u8138\u513f\uff0c\u5174\u594b\u5f97\u4e0d\u5f97\u4e86\uff1b\u800c\u8fd9\u4e24\u5929\u6709\u4e86\u957f\u7bc7\u5e45\u7684\u8bbf\u8c08\u8282\u76ee\uff0c\u5374\u5bf9\u5a92\u4f53\u5931\u53bb\u4e86\u5174\u8da3\u3002\u5c31\u597d\u50cf1997\u5e74\u505a\u4e2a\u4eba\u4e3b\u9875\uff0c\u4ee5\u4e3a\u6574\u4e2a\u4e92\u8054\u7f51\u7684\u4eba\u90fd\u4f1a\u77e5\u9053\u81ea\u5df1\uff0c\u5230\u73b0\u5728\u77e5\u9053\u81ea\u5df1\u6c38\u8fdc\u90fd\u4ec5\u4ec5\u662f\u65e0\u6570\u7684\u72ec\u7279\u7684\u4e2a\u4f53\u7684\u4e00\u5458\uff1b\u800c\u7535\u89c6\uff0c\u4e5f\u5343\u4e07\u4e0d\u8981\u4ee5\u4e3a\u4e0a\u4e86\u7535\u89c6\u5c31\u4f1a\u6709\u4e9b\u4ec0\u4e48\u4e0d\u540c\u3002\u4eca\u5929\uff0c\u6211\u665a\u4e0a\u6709\u7ea6\uff0c\u5c31\u5fd8\u8bb0\u4e86\u4e0a\u7535\u89c6\u8fd9\u7801\u4e8b\u60c5\uff1b\u6587\u5cf0\u53c2\u52a0\u516c\u53f8\u7684\u6d3b\u52a8\uff0c\u665a\u4e0a\u4e0d\u56de\u5bb6\u5403\u996d\uff1b\u9038\u51e1\u7684\u5916\u516c\u5916\u5a46\u56e0\u4e3a\u542c\u4e0d\u61c2\u8282\u76ee\u91cc\u7684\u82f1\u6587\uff0c\u5728\u5468\u4e00\u64ad\u51fa\u7684\u65f6\u5019\u5c31\u76f4\u63a5\u6362\u5230\u4e86\u4e2d\u592e\u53f0\u7684\u300a\u5468\u6069\u6765\u5728\u91cd\u5e86\u300b\uff0c\u800c\u5c0f\u9038\u51e1\u66f4\u662f\u5bf9\u7535\u89c6\u91cc\u7238\u7238\u6ca1\u6709\u4e00\u70b9\u5174\u8da3\uff0c\u5b89\u5fc3\u7684\u73a9\u81ea\u5df1\u7684\u73a9\u5177\u3002\u8fd9\u4e2a\u4e16\u754c\uff0c\u5e76\u6ca1\u6709\u56e0\u4e3a\u81ea\u5df1\u5728\u7535\u89c6\u4e0a\u7684\u51fa\u73b0\u6709\u4efb\u4f55\u53d8\u5316\uff0c\u800c\u5b9e\u8d28\u4e0a\uff0c\u7684\u786e\u6ca1\u6709\u53d8\u5316\uff0c\u4e00\u4e01\u70b9\u53d8\u5316\u4e5f\u6ca1\u6709\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u524d\u51e0\u5929\u8d34\u4e86\u4e24\u4e2a\u6781\u9650\u76f8\u5173\u7684\u95ee\u9898\u3002\u6211\u4ece\u8fd9\u79cd\u5947\u602a\u7684\u95ee\u9898\u91cc\u9762\u5b66\u5230\u7684\uff0c\u548c\u4ee5\u524d\u7684\u201c\u628a\u5927\u8c61\u653e\u8fdb\u51b0\u7bb1\u201d\u7684\u95ee\u9898\u4e00\u6837\uff0c\u4e5f\u662f\u5173\u4e8e\u5b8f\u89c2 … \u7ee7\u7eed\u9605\u8bfb\u5b8f\u89c2\u7684\u601d\u8003\u95ee\u9898 – \u7b2c\u4e8c\u90e8\u5206<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"_links":{"self":[{"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/posts\/266"}],"collection":[{"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/comments?post=266"}],"version-history":[{"count":0,"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/posts\/266\/revisions"}],"wp:attachment":[{"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/media?parent=266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/categories?post=266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.wangjianshuo.com\/cn\/wp-json\/wp\/v2\/tags?post=266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}