{"id":1690,"date":"2021-02-08T19:44:06","date_gmt":"2021-02-08T11:44:06","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1690"},"modified":"2021-02-08T19:44:06","modified_gmt":"2021-02-08T11:44:06","slug":"%e5%9b%9e%e5%9b%bd%e5%b0%8f%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/%e5%9b%9e%e5%9b%bd%e5%b0%8f%e8%ae%b0\/","title":{"rendered":"\u56de\u56fd\u5c0f\u8bb0"},"content":{"rendered":"<h2>\u4f38\u624b\u515a<\/h2>\n<p>\u56de\u56fd\u7684\u822a\u73ed\u4e0a\u60f3\u627e\u70b9\u4e66\u8bfb\u4e00\u8bfb\u6253\u53d1\u4e00\u4e0b\u65e0\u804a\u7684\u98de\u884c\u65f6\u95f4\uff0c\u7b2c\u4e00\u4e2a\u60f3\u5230\u7684\u5c31\u662f\u8ddf\u8fdb\u4e00\u4e0b TAOCP \u5199\u5b8c\u4e86\u6ca1\u6709\uff0c\u7136\u540e\u8d6b\u7136\u53d1\u73b0\u524d\u6bb5\u65f6\u95f4\u627e\u5230\u7684\u90a3\u4e2a\u68d2\u68d2\u7684\u5217\u6709\u6700\u65b0 TAOCP \u5c0f\u518c\u5b50\u7684\u7f51\u7ad9\u5c45\u7136 404 \u4e86\u3002\u4e8e\u662f\u6b63\u597d\u8fd9\u51e0\u5929\u5728\u548c doc \u4ea4\u6d41 pokemon go\uff0c\u611f\u89c9\u4e00\u5b9a\u4f1a\u5f97\u5230\u597d\u7684\u5efa\u8bae\uff0c\u4e8e\u662f\u4ed6\u5f88\u5feb\u5c31\u4e22\u8fc7\u6765\u4e24\u672c\u3002<\/p>\n<blockquote><p>\n  \u6709\u4e2a\u7b80\u5355\u7684\u51e0\u4f55\u4e66\uff0c\u8fd8\u6709\u4e2a\u535a\u5f08\u8bba\u7684\u4e66<br \/>\n  \u4f60\u9009\u4e00\u4e2a\uff1f\n<\/p><\/blockquote>\n<p>\u8fd9\u4e2a\u7b80\u5355\u7684\u51e0\u4f55\u4e66\u6211\u4e00\u770b\u4e66\u540d\u4eba\u5c31\u50bb\u4e86\uff0c\u76f4\u63a5 pass\u3002<br \/>\n\u540e\u8005\u8fd8\u662f\u80fd\u770b\u8fdb\u53bb\u7684\u3002\u3002\u3002<\/p>\n<p>\u70b9\u8fdb\u53bb\u521d\u770b\u600e\u4e48\u611f\u89c9\u884c\u6587\u98ce\u683c\u6709\u70b9\u63a5\u8fd1 TAOCP \u548c\u7a33\u64cd\u80dc\u5238\u3002\u3002\u3002\u7136\u540e\u53d1\u73b0\u4f5c\u8005\u679c\u7136\u662f Conway\u3002\u3002\u3002<\/p>\n<p>\u540e\u6765\u610f\u8bc6\u5230\u539f\u6765\u8fd9\u672c\u5c31\u662f ONAG\u3002\u3002On Numbers and Games (ONAG)\u3002<br \/>\n\u662f\u7a33\u64cd\u80dc\u5238\u7684\u59ca\u59b9\u7bc7\u3002\u3002\u3002<\/p>\n<p>\u5927\u6982 ONAG \u548c\u7a33\u64cd\u80dc\u5238\u7684\u5173\u7cfb\u3002\u3002\u6709\u70b9\u50cf\u662f\u3002\u3002<br \/>\nHTSI \u548c \u6570\u5b66\u4e0e\u731c\u60f3\u3002\u3002\uff08\u521a\u597d\u540e\u8005\u4e5f\u662f\u4e24\u5377\uff09\u3002\u3002<\/p>\n<h2>On Numbers and Games<\/h2>\n<p>ONAG \u8fd9\u672c\u4e66\u5728\u8bb2\u8ff0\u7684\u5176\u5b9e\u5c31\u662f surreal numbers\uff0c<\/p>\n<p>\u4f17\u6240\u5468\u77e5 Knuth \u975e\u5e38\u559c\u6b22\u559c\u6b22 surreal numbers\uff0c\u4e3a\u6b64\u8fd8\u4e13\u95e8\u5199\u4e86\u672c\u5947\u602a\u7684\u5c0f\u8bf4\u3002\u3002<\/p>\n<p>\u6211\u9ad8\u4e00\u7684\u65f6\u5019\u5f53\u505a\u7761\u524d\u8bfb\u7269\u770b\u8fc7\u4e00\u904d\u3002\u3002\u4f46\u662f\u663e\u7136\u6ca1\u8bfb\u61c2\u3002\u3002\u3002<br \/>\n\u539f\u6765\u6b63\u786e\u7684\u59ff\u52bf\u662f\u5148\u8bfb ONAG \u554a\u3002\u3002\u3002<\/p>\n<p>\u5f53\u7136\u5728\u6210\u4e66\u7684\u65f6\u5019\uff0c\u8fd8\u6ca1\u6709 Surreal numbers \u8fd9\u4e2a\u540d\u5b57\u3002<br \/>\nConway \u5728\u4e66\u4e2d\u76f4\u63a5\u4f7f\u7528\u4e86 Game \u8fd9\u4e2a\u540d\u5b57\u3002\u3002\u3002<\/p>\n<p>\u6ca1\u9519 Conway \u8ba4\u4e3a Game \u662f Number \u7684\u4e00\u79cd\u63a8\u5e7f\u3002\u3002<br \/>\n\u5e76\u7528 Game \u6765\u91cd\u65b0\u7406\u89e3 Number\u3002\u3002<\/p>\n<p>\u4e66\u7684\u7ed3\u6784\u5f88\u7b80\u5355\uff0c\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\u3002\u3002<\/p>\n<p>\u7b2c\u4e00\u90e8\u5206\u4ecb\u7ecd\u62bd\u8c61\u7684 Surreal Numbers\uff08\u7531\u4e8e Game \u8fd9\u4e2a\u540d\u5b57\u5bb9\u6613\u5f15\u8d77\u6b67\u4e49\uff0c\u4e0b\u6587\u8fd8\u662f\u7528 Surreal Number \u6765\u7279\u6307\u4e66\u4e2d\u6240\u8ff0\u7684\u8fd9\u79cd\u4ee3\u6570\u7ed3\u6784\uff09\u3002\u3002\u3002<br \/>\n\u5e76\u4e14\u7528 Surreal Numbers \u6765\u964d\u7ef4\u6253\u51fb\uff0c\u6765\u5f97\u5230\u5176\u4ed6\u6240\u6709\u6211\u4eec\u5df2\u77e5\u7684\u6570\u3002<\/p>\n<p>\u7b2c\u4e8c\u90e8\u5206\u4ecb\u7ecd Surreal Numbers \u5728\u7ec4\u5408\u6e38\u620f\u91cc\u7684\u4e00\u4e9b\u5177\u4f53\u5e94\u7528\u3002<\/p>\n<h3>Surreal Numbers<\/h3>\n<p>\u9664\u4e86\u6536\u5230\u7ec4\u5408\u6e38\u620f\u7684\u542f\u53d1\uff0cSurreal Numbers \u53e6\u4e00\u4e2a\u6765\u6e90\u5c31\u662f\u5bf9\u6234\u5fb7\u91d1\u5206\u5272\u7684\u91cd\u65b0\u5ba1\u89c6\u3002<\/p>\n<p>\u9996\u5148\u56de\u987e\u5b9e\u6570<\/p>\n<p>\u6211\u4eec\u4e0d\u4ec5\u8981\u6570\u5355\u4e2a\u7684\u5bf9\u8c61\uff0c\u800c\u4e14\u4e5f\u9700\u8981\u5ea6\u91cf\u50cf\u957f\u5ea6\u3001\u9762\u79ef\u91cd\u91cf\u548c\u65f6\u95f4\u8fd9\u6837\u7684\u91cf\uff0c\u4eba\u4eec\u5f88\u65e9\u5c31\u4f7f\u7528\u5206\u6570\u548c\u6bd4\u6765\u8868\u793a\u4e24\u4e2a\u91cf\u4e4b\u95f4\u7684\u5ea6\u91cf\u5173\u7cfb\uff0c\u76f4\u5230\u6700\u540e\u8fc8\u51fa\u5177\u6709\u51b3\u5b9a\u6027\u7684\u4e00\u6b65\uff0c<\/p>\n<blockquote><p>\n  \u65e2\uff1a\u7b26\u53f7 m\/n \u8131\u79bb\u4e86\u5b83\u540c\u6d4b\u91cf\u8fc7\u7a0b\u4e2d\u53ca\u88ab\u6d4b\u91cf\u7684\u91cf\u7684\u5177\u4f53\u5173\u7cfb\uff0c\u800c\u88ab\u770b\u4f5c\u662f\u4e00\u79cd\u7eaf\u7cb9\u7684\u6570\uff0c\u5b83\u672c\u8eab\u4f5c\u4e3a\u4e00\u4e2a\u5b9e\u4f53\u4e0e\u81ea\u7136\u6570\u6709\u540c\u6837\u7684\u5730\u4f4d\u3002\u5f53 m \u548c n \u662f\u81ea\u7136\u6570\u65f6\uff0c\u7b26\u53f7 m\/n \u79f0\u4e3a\u6709\u7406\u6570\u3002\n<\/p><\/blockquote>\n<p>\u4e4b\u540e\u53e4\u5e0c\u814a\u4eba\u6700\u60ca\u4eba\u7684\u53d1\u73b0\u53ef\u80fd\u5c31\u662f\u53d1\u73b0\u4e86\u4e0d\u53ef\u516c\u5ea6\u7ebf\u6bb5\u3002\u3002\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u719f\u77e5\u7684\u65e0\u7406\u6570\uff0c\u6700\u7b80\u5355\u7684\u65e0\u7406\u6570\u5c31\u662f\u5355\u4f4d\u6b63\u65b9\u5f62\u7684\u5bf9\u89d2\u7ebf\u3002sqrt(2) \u4e86\u3002<\/p>\n<blockquote><p>\n  \u5728\u6b27\u51e0\u91cc\u5f97\u7684\u539f\u672c\uff08Elements\uff09\u4e2d\uff0c\u4ee5\u51e0\u4f55\u5f62\u5f0f\u51fa\u73b0\u7684\u6b27\u591a\u514b\u65af\uff08Eudoxus\uff09\u7684\u4e0d\u53ef\u516c\u5ea6\u7406\u8bba\u662f\u5e0c\u814a\u6570\u5b66\u7684\u6770\u4f5c\u3002\u76f4\u5230 19 \u4e16\u7eaa\u672b\u671f\uff0c\u5728\u6234\u5fb7\u91d1\u3001\u5eb7\u6258\u548c\u7ef4\u5c14\u65af\u7279\u62c9\u65af\u5efa\u7acb\u4e86\u65e0\u7406\u6570\u7684\u4e25\u683c\u7406\u8bba\u4e4b\u540e\uff0c\u6b27\u591a\u514b\u65af\u7684\u8fd9\u4e2a\u7406\u8bba\u624d\u5145\u5206\u88ab\u4eba\u7406\u89e3\u3002\u6211\u4eec\u5c06\u7528\u73b0\u4ee3\u7b97\u672f\u65b9\u6cd5\u6765\u8bf4\u660e\u8fd9\u4e2a\u7406\u8bba\u3002\n<\/p><\/blockquote>\n<p>\u5173\u4e8e\u65e0\u7406\u6570\u7684\u5b9a\u4e49\u6709\u5f88\u591a\u79cd\uff0cConway \u5355\u72ec\u62ce\u51fa\u6765\u8bf4\u7684\u662f\u6234\u5fb7\u91d1\u5206\u5272\u3002<\/p>\n<h3>\u6234\u5fb7\u91d1\u5206\u5272<\/h3>\n<ul>\n<li>\u5047\u8bbe\u7ed9\u5b9a\u67d0\u79cd\uff0c\u628a\u5168\u4f53\u6709\u7406\u6570\u96c6\u5206\u4e3a\u4e24\u4e2a\u96c6\u5408 L \u548c R\uff0c\u4f7f R<br \/>\n\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20 r\uff0c\u5927\u4e8e L \u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20 l\u3002\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u8fd9\u6837\u7684\u5206\u5272\uff0c\u5b58\u5728\u7740\u4e09\u79cd\u53ef\u80fd\uff0c\u5176\u4e2d\u6709\u4e14\u4ec5\u6709\u4e00\u79cd\u6210\u7acb\u3002<\/li>\n<\/ul>\n<ol>\n<li>L \u6709\u6700\u5927\u5143\u7d20<\/li>\n<li>R \u6709\u6700\u5c0f\u5143\u7d20<\/li>\n<li>L \u6ca1\u6709\u6700\u5927\u5143\u7d20\u4e14 R \u6ca1\u6709\u6700\u5c0f\u5143\u7d20<\/li>\n<\/ol>\n<p>\u5176\u4e2d\u7b2c\u4e09\u79cd\u60c5\u51b5\uff0c\u51fa\u73b0\u4e86\u4e00\u4e2a\u6709\u7406\u6570\u4e4b\u95f4\u7684 gap\uff0c\u800c\u8fd9\u4e2a gap \u552f\u4e00\u786e\u5b9a\u4e86\u4e00\u4e2a\u65e0\u7406\u6570\u3002<\/p>\n<p>\u76f8\u6bd4\u5176\u4ed6\u65b9\u6cd5\uff08\u533a\u95f4\u5957\u3001\u65e0\u9650\u4e0d\u5faa\u73af\u5c0f\u6570\uff09\uff0c\u6234\u5fb7\u91d1\u5206\u5272\u6d89\u53ca\u66f4\u9ad8\u7a0b\u5ea6\u7684\u62bd\u8c61\uff0c\u56e0\u4e3a\u5b83\u5bf9\u786e\u5b9a\u96c6\u5408 L \u548c R \u7684\u89c4\u5219\u6ca1\u6709\u52a0\u4ee5\u9650\u5236\u3002<\/p>\n<h3>Conway \u5bf9\u6234\u5fb7\u91d1\u5206\u5272\u7684\u6279\u5224<\/h3>\n<p>Conway \u8bf4\u6234\u5fb7\u91d1\u5206\u5272\u6700\u6709\u95ee\u9898\u7684\u7684\u5730\u65b9\u662f\uff0c<\/p>\n<blockquote><p>\n  Perhaps the most important is that the rationals are supposed to have been already constructed in some other way, and yet are &#8220;recounstructed&#8221; as centain real numbers. The distincion between the \u201cold\u201d and \u201cnew\u201d rationals seems artificial but essential.\n<\/p><\/blockquote>\n<p>\u5929\u5436\u565c\uff0c\u8fd9\u56db\u820d\u4e94\u5165\u5c31\u662f\u8bf4\u4eba\u5bb6\u5728\u641e\u300c\u5faa\u73af\u8bba\u8bc1\u300d\u554a\uff01<\/p>\n<h3>\u4e09\u751f\u4e07\u7269<\/h3>\n<p>\u6240\u4ee5 Conway \u5b8c\u5168\u820d\u5f03\u4e86\u5bf9\u6709\u7406\u6570\u5148\u9a8c\u4f9d\u8d56<br \/>\n\u8ba9\u4e00\u5207\u4ece 0 \u5f00\u59cb\u3002\u3002\u5f00\u59cb\u4e86\u4e0a\u5e1d\u9020\u6570\u7684\u4e03\u5206\u949f\u3002\u3002\u3002<\/p>\n<p>\uff08\u987a\u4fbf\u8fd8\u53bb\u6389\u4e86 L \u548c R \u5fc5\u987b\u6709\u5e8f\u7684\u9650\u5236\u3002\u3002\uff09<\/p>\n<p>Q\uff1aSurreal Numbers \u548c Real Number \u7684\u5173\u7cfb\uff1f<br \/>\nA\uff1a\u524d\u8005\u53ef\u4ee5\u89c6\u4e3a\u540e\u8005\u7684\u63a8\u5e7f\uff0c\u53bb\u6389\u4e86\u4e0a\u9762 L \u548c R \u5fc5\u987b\u6709\u5e8f\u7684\u9650\u5236\uff0c\u4f7f\u5f97 Surreal Numbers \u4e0d\u662f\u5168\u5e8f\u7684\u3002\u3002<\/p>\n<p>Q\uff1aSurreal Numbers \u548c Nim \u53d6\u5b50\u6e38\u620f\u7684\u5173\u7cfb\uff1f<br \/>\nA\uff1a\u524d\u8005\u53ef\u4ee5\u89c6\u4e3a\u540e\u8005\u7684\u63a8\u5e7f\uff0c\u552f\u4e00\u7684\u533a\u522b\u5c31\u662f Nim \u53d6\u5b50\u6e38\u620f\u662f Impartial Game\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4e00\u4e2a\u7279\u5b9a\u7684\u72b6\u6001\uff0c\u5f53\u524d\u65e0\u8bba\u8f6e\u5230\u8c01\u8d70\uff0cAlice \u548c Bob \u6240\u80fd\u91c7\u53d6\u7684\u51b3\u7b56\u662f\u4e00\u6837\u7684\u3002<\/p>\n<p>\u6700\u540e\u6211\u89c9\u5f97\u5168\u4e66\u6700\u6709\u610f\u601d\u7684\u5c31\u662f\u5377\u9996\u7684\u8fd9\u4e2a\u4f9d\u8d56\u56fe\u3002\u3002\u3002<br \/>\n\u7b2c\u4e00\u6b21\u770b\u8fc7\u53bb\u5b8c\u5168\u4e91\u91cc\u96fe\u91cc\u3001\u4e0d\u77e5\u6240\u4e91\u3002\u3002<\/p>\n<p>\u8bfb\u5b8c\u4e4b\u540e\u624d\u80fd\u53d1\u73b0\u6b64\u56fe\u4e2d\u7684\u5965\u5999\u3002\u3002\u3002<\/p>\n<h2>\u56de\u56fd\u4e4b\u540e<\/h2>\n<p>\u8fd9\u6837\u770b\u8d77\u6765\u6211\u4eca\u5e74\u7684\u7b2c\u4e00\u4e2a OKR \u8c8c\u4f3c\u5c31\u5df2\u7ecf\u5b8c\u6210\u4e86\uff01\u603b\u7b97\u53ef\u4ee5\u548c\u5bb6\u4eba\u56e2\u805a\u5566\uff01<\/p>\n<p>\u81f3\u4e8e\u56de\u56fd\u4e4b\u884c\u672c\u8eab\u3002\u3002\u5176\u5b9e\u5b9e\u5728\u6ca1\u5565\u503c\u5f97\u7ee7\u7eed\u63cf\u8ff0\u7684\u3002\u3002\u3002<br \/>\n\u6211\u6240\u906d\u9047\u4e4b\u6df7\u6c8c\u3002\u3002\u53ef\u80fd\u662f\u8fd9\u4e2a\u65f6\u671f\u6bcf\u4e2a\u4eba\u90fd\u5fc5\u987b\u9762\u5bf9\u7684\u4e00\u95e8\u5fc5\u4fee\u8bfe\u3002\u3002<\/p>\n<p>\u8fd8\u8bb0\u5f97\u5269\u4f59\u4ef7\u503c\u53bb\u5e74\u6700\u540e\u90a3\u4e00\u671f\u6240\u8bf4\uff0c\u5065\u5eb7\u7801\u5c31\u662f\u8fd9\u4e2a\u65f6\u4ee3\u7684\u516c\u6c11\u8eab\u4efd\u3002\u3002\u73b0\u5728\u81ea\u5df1\u5bf9\u516c\u6c11\u8eab\u4efd\u6709\u4e86\u5168\u65b0\u7684\u7406\u89e3\u4e86\u5417\uff1f<br \/>\n\u5f53\u7136\u6211\u89c9\u5f97\u975e\u5e38\u65f6\u671f\u5404\u79cd\u63aa\u65bd\u90fd\u662f\u5fc5\u8981\u7684\u3002\u3002<br 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