{"id":34755,"date":"2019-12-17T00:22:08","date_gmt":"2019-12-16T16:22:08","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=34755"},"modified":"2019-12-16T09:49:25","modified_gmt":"2019-12-16T01:49:25","slug":"%e5%be%ae%e7%a9%8d%e5%88%86%e7%9a%84dx%e4%b8%80%ef%bc%9a%e7%84%a1%e9%99%90%e5%b0%8f%e6%95%b8%e8%88%87%e9%9d%9e%e6%a8%99%e6%ba%96%e5%88%86%e6%9e%90%e5%ad%b8","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=34755","title":{"rendered":"\u5fae\u7a4d\u5206\u7684dx(\u4e00)\uff1a\u7121\u9650\u5c0f\u6578\u8207\u975e\u6a19\u6e96\u5206\u6790\u5b78"},"content":{"rendered":"

17\u4e16\u7d00\u6642\u725b\u9813\u548c\u840a\u5e03\u5c3c\u8332\u767c\u660e\u4e86\u5fae\u7a4d\u5206\u3002\u5176\u4e2d\u840a\u5e03\u5c3c\u8332\u7684\u300c\u7a4d\u5206\u7b26\u865f\u300d\u222b\u3001\u300c\u6975\u5fae\u5c0f\u5dee\u300ddx \u7b49\u5169\u500b\u7b26\u865f\u4ecd\u7136\u4f7f\u7528\u81f3\u4eca\u3002\u73fe\u4eca\u7684\u8ab2\u672c\u6703\u7528\u300c\u6975\u9650\u300d\u89e3\u91cb\uff0c\u6240\u4ee5\u6709\u4e9b\u4eba\u8aaa dx \u53ea\u662f\u7b26\u865f\uff0c\u4e0d\u9700\u8981\u5be6\u8cea\u610f\u7fa9\u3002\u9019\u5169\u7a2e\u89c0\u9ede\u90fd\u6709\u5176\u610f\u7fa9\u548c\u91cd\u8981\u6027\u3002\u672c\u6587\u5c07\u5206\u70ba\u82e5\u5e72\u671f\uff0c\u5f9e\u4e0d\u540c\u89c0\u9ede\u63a2\u7d22\u5fae\u7a4d\u5206\u7684\u9748\u9b42\u3001\u4ee5\u53ca\u5404\u89c0\u9ede\u7684\u61c9\u7528\u3002<\/strong><\/span><\/p>\n

\u64b0\u6587\uff5c\u674e\u9f8d\u6b23<\/strong><\/p>\n

\u25cf\u70ba\u4f55\u6709\u5fae\u7a4d\u5206<\/strong><\/span><\/p>\n

\u81ea\u53e4\u4ee5\u4f86\uff0c\u6578\u5b78\u5bb6\u5011\u5c31\u6df1\u77e5\u81ea\u7136\u842c\u7269\u96e3\u4ee5\u6e2c\u91cf\uff0c\u800c\u4e0d\u5982\u5713\u5f62\u3001\u591a\u908a\u5f62\u3001\u6a62\u5713\u4e00\u822c\u7c21\u6f54\u3002\u6211\u5011\u56fa\u7136\u53ef\u4ee5\u62ff\u8d77\u4e00\u628a\u5c3a\u958b\u59cb\u8010\u8457\u6027\u5b50\u91cf\uff0c\u4f8b\u5982\u963f\u57fa\u7c73\u5fb7 (\u0391\u03c1\u03c7\u03b9\u03bc\u03ae\u03b4\u03b7\u03c2 \u03bf \u03a3\u03c5\u03c1\u03b1\u03ba\u03bf\u03cd\u03c3\u03b9\u03bf\u03c2)\u3001\u5289\u5fbd\u3001\u95dc\u5b5d\u548c (\u95a2 \u5b5d\u548c) \u7684\u5272\u5713\u8853\uff0c\u53c8\u8b6c\u5982\u53e4\u5df4\u6bd4\u502b\u4eba\u7684\u4e09\u89d2\u51fd\u6578\u8868\uff0c\u90fd\u662f\u6e2c\u91cf\u7684\u5178\u7bc4\u548c\u5148\u9a45\u3002\u96d6\u7136\u4ee5\u4eba\u985e\u7684\u529b\u91cf\u548c\u58fd\u547d\uff0c\u5fc5\u5b9a\u6703\u7559\u4e0b\u8aa4\u5dee\uff0c\u4f46\u662f\u53ea\u8981\u6211\u5011\u9858\u610f\u518d\u91cf\u5e7e\u6b21\uff0c\u5c31\u53ef\u4ee5\u628a\u8aa4\u5dee\u4e00\u76f4\u7e2e\u5c0f\u3002\u6240\u4ee5\u7406\u60f3\u4e0a\u7684\u8aa4\u5dee\u662f\u300c\u7121\u9650\u5c0f\u7684\u6578 (infinitesimal number)\u300d\uff0c\u8207\u7121\u9650\u5927\u76f8\u5c0d\u300217\u4e16\u7d00\uff0c\u52d2\u5167\uff0e\u7b1b\u5361\u5152 (Ren\u00e9 Descartes) \u767c\u660e\u89e3\u6790\u5e7e\u4f55\uff0c\u518d\u6b21\u5e36\u52d5\u4e86\u7121\u9650\u5c0f\u6578\u7684\u8a0e\u8ad6\u3002\u9019\u9580\u5b78\u554f\u88ab\u7a31\u505a\u300c\u5206\u6790\u5b78 (analysis)\u300d\u6216\u300c\u6578\u5b78\u5206\u6790 (mathematical analysis)\u300d\u3002\u7d42\u65bc\u5728\u540c\u4e00\u4e16\u7d00\uff0c\u827e\u85a9\u514b\uff0e\u725b\u9813 (Isaac Newton)\u3001\u54e5\u7279\u4f5b\u840a\u5fb7\uff0e\u840a\u5e03\u5c3c\u8332 (Gottfried Leibniz) \u78ba\u7acb\u4e86\u5206\u6790\u5b78\u7684\u57fa\u790e\u3002\u6240\u4ee5\u4ed6\u5011\u88ab\u5c0a\u70ba\u5fae\u7a4d\u5206\u7684\u767c\u660e\u8005\u8a3b1<\/sup>\u3002<\/p>\n

\u25cf\u7121\u9650\u5927\u8207\u7121\u9650\u5c0f<\/strong><\/span><\/p>\n

\u300c\u7121\u9650\u300d\u7684\u6982\u5ff5\u592a\u96e3\u63cf\u7e6a\uff0c\u4f46\u4e5f\u56e0\u6b64\u800c\u8ff7\u4eba\u3002\u300c\u7121\u9650\u5927\u300d\u662f\u4ec0\u9ebc\u5462\uff1f\u7121\u9650\u5927\u6e1b\u4e00\u662f\u4ec0\u9ebc\uff1f\u7121\u9650\u5927\u6e1b\u7121\u9650\u5927\u662f\u4ec0\u9ebc\uff1f\u300c\u7121\u9650\u5927\u300d\u5df2\u7d93\u5920\u96e3\u4e86\uff0c\u300c\u7121\u9650\u5c0f\u300d\u537b\u66f4\u96e3\u3002\u6211\u5011\u6216\u8a31\u80fd\u60f3\u50cf\u5728\u6578\u7dda\u770b\u4e0d\u5230\u7684\u5730\u65b9\u6709\u500b\u76e1\u982d\uff0c\u90a3\u88e1\u7684\u6578\u5b57\u53eb\u505a\u7121\u9650\u5927\u3002\u7121\u9650\u5c0f\u537b\u662f\u786c\u751f\u751f\u5730\u5728\u6211\u5011\u773c\u524d\u6d88\u5931\u3002\u7121\u9650\u5c0f\u5728\u6578\u7dda\u7684\u4f4d\u7f6e\u61c9\u8a72\u548c 0 \u4e00\u6a21\u4e00\u6a23\uff0c\u53ef\u662f\u7121\u9650\u5c0f\u53c8\u4e0d\u662f 0\uff01<\/p>\n

\u25cf\u8d85\u5be6\u6578<\/strong><\/span><\/p>\n

\u5fae\u7a4d\u5206\u767c\u660e\u4e4b\u521d\uff0c\u4ecd\u662f\u4ee5\u7121\u9650\u5c0f\u63cf\u8ff0\uff0c\u56e0\u6b64\u5341\u5206\u96e3\u4ee5\u7406\u89e3\u3002\u5230\u4e8619\u4e16\u7d00\u521d\uff0c\u5f9e\u840a\u5e03\u5c3c\u8332\u7684\u7406\u8ad6\u4e2d\u767c\u5c55\u51fa\u4e86\u300c\u6975\u9650 (limit)\u300d\u7684\u6982\u5ff5\u3002\u6b64\u8209\u63a8\u7ffb\u4e86\u904e\u5f80\u7684\u8a0e\u8ad6\uff0c\u6368\u68c4\u4e86\u7121\u9650\u5c0f\u7684\u60f3\u6cd5\u3002\u540c\u4e00\u4e16\u7d00\uff0c\u908f\u8f2f\u5b78\u767c\u5c55\u8d77\u4f86\u4e4b\u5f8c\uff0c\u8ffd\u6c42\u56b4\u8b39\u7684\u6d6a\u6f6e\u66f4\u8b93\u7121\u9650\u5c0f\u88ab\u6253\u5165\u51b7\u5bae\u3002<\/p>\n

\u76f4\u52301960\u5e74\u4ee3\uff0c\u4e9e\u4f2f\u62c9\u7f55\uff0e\u9b6f\u8cd3\u905c (Abraham Robinson) \u904b\u7528\u908f\u8f2f\u5b78\u8b49\u660e\u8a3b2<\/sup>\u53ef\u4ee5\u628a\u5be6\u6578\u300c\u64f4\u5145\u300d\u800c\u4e0d\u7522\u751f\u4efb\u4f55\u77db\u76fe\u3002\u76f8\u5c0d\u65bc\u5df2\u7d93\u666e\u53ca\u7684\u6975\u9650\u7406\u8ad6\uff0c\u6d74\u706b\u91cd\u751f\u7684\u7121\u9650\u5c0f\u7406\u8ad6\u88ab\u7a31\u70ba\u300c\u975e\u6a19\u6e96\u5206\u6790\u5b78 (nonstandard analysis)\u300d\u3002\u9b6f\u8cd3\u905c\u4ee5 R \u4ee3\u8868\u5be6\u6578 (real numbers)\uff0c*R \u8868\u793a\u64f4\u5145\u5f8c\u7684\u5be6\u6578\uff0c\u53c8\u7a31\u70ba\u8d85\u5be6\u6578 (hyperreal numbers)\u3002\u51e1\u662f\u5728 R \u6210\u7acb\u7684\u4e00\u968e\u908f\u8f2f (first order logic) \u547d\u984c\uff0c\u5728 *R \u4e5f\u6703\u6210\u7acb\u3002\u4f8b\u5982\uff1a<\/p>\n

\uff0e\u5177\u6709\u56db\u5247\u904b\u7b97\u3002(\u4efb\u5169\u6578\u53ef\u76f8\u52a0\u3001\u6e1b\u3001\u4e58\uff0c\u82e5\u7b2c\u4e8c\u500b\u6578\u4e0d\u662f 0 \u53ef\u4ee5\u76f8\u9664)<\/p>\n

\uff0e\u4efb\u5169\u6578\u80fd\u6bd4\u5927\u5c0f\uff0c\u4e14\u6b63\u6578\u7684\u52a0\u6cd5\u3001\u4e58\u6cd5\u4fdd\u6301\u5927\u5c0f\u95dc\u4fc2\u3002<\/p>\n

\u5728 *R \u4e2d\uff0c\u6bd4\u6240\u6709\u5be6\u6578\u90fd\u5927\u7684\u6578\u8a3b3<\/sup>\uff0c\u662f\u6b63\u7121\u9650\u5927\uff1b\u6bd4\u6240\u6709\u5be6\u6578\u90fd\u5c0f\u7684\u6578\uff0c\u662f\u8ca0\u7121\u9650\u5927\uff1b\u4ecb\u65bc\u5169\u500b\u5be6\u6578\u4e4b\u9593\u7684\u6578\uff0c\u662f\u6709\u9650\u6578(\u5305\u542b\u7121\u9650\u5c0f\u6578)\uff1b\u6bd4\u6240\u6709\u6b63\u5be6\u6578\u90fd\u5c0f\u53c8\u6bd4\u6240\u6709\u8ca0\u5be6\u6578\u90fd\u5927\u7684\u6578\u8a3b3<\/sup>\uff0c\u662f\u7121\u9650\u5c0f(\u5305\u542b 0)\u3002\u76f4\u89ba\u4e0a\u6c92\u6709\u4ec0\u9ebc\u77db\u76fe\u7684\u904b\u7b97\u898f\u5247\u5927\u6982\u90fd\u6703\u6210\u7acb\uff0c\u4f8b\u5982\uff1a<\/p>\n

\uff0e[\u6b63\u7121\u9650\u5927 \u52a0 \u6b63\u7121\u9650\u5927] \u662f \u6b63\u7121\u9650\u5927<\/p>\n

\uff0e[\u6709\u9650 \u9664\u4ee5 \u7121\u9650\u5927] \u662f \u7121\u9650\u5c0f<\/p>\n

\u5728\u725b\u9813\u3001\u840a\u5e03\u5c3c\u8332\u7684\u7406\u8ad6\u4e2d\uff0c\u90fd\u6709\u628a\u7121\u9650\u5c0f\u6578\u7701\u7565\u7684\u6b65\u9a5f\u3002\u5728 *R \u4e2d\u53ef\u4ee5\u7528\u9019\u500b\u5b9a\u7406\u89e3\u91cb\uff1a<\/p>\n

\uff0e\u4efb\u4f55\u6709\u9650\u6578 x \u90fd\u80fd\u552f\u4e00\u5730\u5206\u6210\u4e00\u500b\u5be6\u6578\u548c\u4e00\u500b\u7121\u9650\u5c0f\u6578\u7684\u548c\u3002\u5176\u4e2d\u7684\u5be6\u6578\u8a18\u70ba st(x)\uff0c\u7a31\u70ba x \u7684\u6a19\u6e96\u90e8\u5206 (standard part)\u3002<\/p>\n

\"\"
\u57161\uff1a\u4efb\u4e00\u500b\u5be6\u6578\u52a0\u4e0a\u7121\u9650\u5c0f\u6578\u7684\u7d50\u679c\u90fd\u5728\u539f\u5148\u7684\u5be6\u6578\u9644\u8fd1\u3002\u5716\u7247\u4f86\u6e90\uff1a\u540c\u53c3\u8003\u8cc7\u6599[4]\uff0c\u7b2c1\u7ae0\u7b2c4\u7bc0\u3002<\/figcaption><\/figure>\u81f3\u65bc\u9023\u7e8c\u51fd\u6578\u3001\u5fae\u5206\u3001\u7a4d\u5206\u53ef\u4ee5\u5982\u6b64\u5b9a\u7fa9\uff1a\u8a3b4<\/sup><\/p>\n

\uff0e\u82e5 st(x)=c \u5247\u6709 st(f(x))=f(c)\uff0c\u5247\u7a31 f(x) \u5728 c \u9023\u7e8c\u3002<\/p>\n

\uff0e\u7d66\u5b9a\u7121\u9650\u5c0f\u6578 dx\u22600\uff0cf(x) \u5728 x=c \u7684\u5fae\u5206\u5b9a\u70ba\"\" (\u82e5\u7d50\u679c\u8ddf\u6211\u5011\u6240\u9078\u7684 dx \u7121\u95dc\u5247\u53ef\u5fae\u5206)<\/p>\n

\uff0e\u03c9 \u70ba\u7121\u9650\u5927\u6574\u6578\u8a3b5<\/sup>\uff0ca=x0<\/sub><\u03be1<\/sub><x1<\/sub><\u03be2<\/sub><x2<\/sub><...<x\u03c9-1<\/sub><\u03be\u03c9<\/sub><x\u03c9<\/sub>=b \u4f7f\u5f97 st(xn<\/sub>-xn-1<\/sub>)=0\uff0c\u5247 f(x) \u5728 [a,b] \u7684\u7a4d\u5206\u5b9a\u70ba\"\"\u8a3b6<\/sup> (\u9023\u7e8c\u51fd\u6578\u90fd\u53ef\u7a4d\u5206)<\/p>\n

\u9b6f\u8cd3\u905c\u4ee5\u6b64\u91cd\u65b0\u8a6e\u91cb\u4e86\u5f88\u591a\u65e2\u6709\u7684\u7d50\u679c\uff0c\u53ef\u8aaa\u662f\u53ea\u8981\u8ddf\u5be6\u6578\u6709\u95dc\u7684\u5b78\u79d1\u90fd\u88ab\u6db5\u84cb\u5230\u4e86\u3002<\/p>\n

\u25cf\u767c\u5c55<\/span><\/strong><\/p>\n

\u9019\u9805\u6210\u5c31\u7121\u975e\u63d0\u4f9b\u4e86\u4e00\u500b\u6709\u8da3\u7684\u89c0\u9ede\uff0c\u6545\u4e5f\u6709\u64c1\u8b77\u8005\uff0c\u5176\u4e2d\u66f4\u6709\u4eba\u628a\u7406\u8ad6\u90e8\u5206\u7a0d\u5fae\u7c21\u5316\u3002\u53ea\u4e0d\u904e\u6279\u8a55\u81ea\u7136\u662f\u5c11\u4e0d\u4e86\uff0c\u4f8b\u5982\uff1a\u4f7f\u7528\u4e86\u9078\u64c7\u516c\u7406\u3001\u908f\u8f2f\u5b78\u592a\u6df1\u5967\u3001\u7121\u6cd5\u69cb\u9020\u7b49\u7b49\u3002\u800c\u6578\u5b78\u7684\u767c\u5c55\u5f9e\u4f86\u4e0d\u662f\u70ba\u4e86\u6d88\u5f2d\u4e0d\u540c\u89c0\u9ede\u4e4b\u9593\u7684\u9d3b\u6e9d\uff0c\u800c\u662f\u8981\u904b\u7528\u5404\u7a2e\u89c0\u9ede\u4f86\u89e3\u6c7a\u554f\u984c\u3002<\/p>\n

 <\/p>\n

\u8a3b\u89e3:<\/strong><\/p>\n

[1] \u5f8c\u4f86\u4e8c\u4eba\u70ba\u6b64\u4e92\u76f8\u6307\u63a7\u527d\u7aca\uff0c\u53ef\u53c3\u8003\uff1c\u8ab0\u662f\u53d7\u5bb3\u8005<\/a>\uff1e\u3002
\n[2] \u9700\u8981\u627f\u8a8d\u9078\u64c7\u516c\u7406\u3002
\n[3] \u9700\u6ce8\u610f\u7121\u9650\u5927\u4e0d\u662f\u4e00\u500b\u6578\u3002\u9019\u7a2e\u6578\u6709\u5f88\u591a(\u7121\u9650\u591a\u500b)\u3002\u7121\u9650\u5c0f\u4e5f\u662f\u3002
\n[4] \u5728\u524d\u5169\u689d\u4e2d\uff0cf(x) \u70ba\u958b\u5340\u9593 (a,b) \u4e0a\u7684\u51fd\u6578\uff1b\u5f8c\u4e00\u689d\u5247\u5728\u9589\u5340\u9593 [a,b] \u4e0a\uff1ba<c<b \u70ba\u4e09\u500b\u4e0d\u540c\u7684\u5be6\u6578\u3002
\n[5] \u70ba\u6b63\u6574\u6578\u7684\u64f4\u5145\uff0c\u53ef\u53c3\u898b\u53c3\u8003\u8cc7\u6599[4]\uff0c\u7b2c3\u7ae0\u7b2c8\u7bc0\u3002
\n[6] \u5c07\u300c\u52a0\u7e3d\u300d\u7684\u52d5\u4f5c\u8996\u70ba\u4e00\u500b\u51fd\u6578\uff0c\u7136\u5f8c\u5c07\u6b64\u51fd\u6578\u64f4\u5145\u5230\u7121\u9650\u5927\u3002<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><\/p>\n

[1] \u300aA History of Mathematics\u300b\u3002F. Cajori \u8457\u3002\u7b2c\u4e8c\u7248(1961)\u3002Macmillan \u51fa\u7248(\u7d10\u7d04)\u3002
\n<\/strong>[2] \u300aNon-Standard Analysis\u300b\u3002A. Robinson \u8457\u3002\u521d\u7248(1966)\u3002North-Holland \u51fa\u7248(\u963f\u59c6\u65af\u7279\u4e39)\u3002
\n[3] \u300aLectures on the Hyperreals: An Introduction to Nonstandard Analysis\u300b\u3002R. Goldblatt \u8457\u3002\u521d\u7248(1998)\u3002Springer-Verlag \u51fa\u7248(\u7d10\u7d04\/\u67cf\u6797\/\u6d77\u5fb7\u5821)\u3002
\n[4] \u300aElementary Calculus: An Infinitesimal Approach\u300b\u3002H. Keisler \u8457\u30022019\u5e749\u6708\u4fee\u8a02\u7248\u3002\u65bc\u7db2\u8def\u514d\u8cbb\u516c\u958b\u3002\u7db2\u5740\uff1ahttp:\/\/www.math.wisc.edu\/~keisler\/calc.html<\/a>\u3002\u53e6\u6709\u5370\u5237\u7248\uff1a\u7b2c\u4e09\u7248(2012)\u3002Dover \u51fa\u7248(\u7d10\u7d04)\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

17\u4e16\u7d00\u6642\u725b\u9813\u548c\u840a\u5e03\u5c3c\u8332\u767c\u660e\u4e86\u5fae\u7a4d\u5206\u3002\u5176\u4e2d\u840a\u5e03\u5c3c\u8332\u7684\u300c\u7a4d\u5206\u7b26\u865f\u300d\u222b\u3001\u300c\u6975\u5fae\u5c0f\u5dee\u300ddx \u7b49\u5169\u500b\u7b26\u865f\u4ecd\u7136\u4f7f\u7528\u81f3\u4eca\u3002\u73fe\u4eca\u7684\u8ab2\u672c\u6703\u7528\u300c\u6975\u9650\u300d\u89e3\u91cb\uff0c\u6240\u4ee5\u6709\u4e9b\u4eba\u8aaa dx \u53ea\u662f\u7b26\u865f\uff0c\u4e0d\u9700\u8981\u5be6\u8cea\u610f\u7fa9\u3002\u9019\u5169\u7a2e\u89c0\u9ede\u90fd\u6709\u5176\u610f\u7fa9\u548c\u91cd\u8981\u6027\u3002\u672c\u6587\u5c07\u5206\u70ba\u82e5\u5e72\u671f\uff0c\u5f9e\u4e0d\u540c\u89c0\u9ede\u63a2\u7d22\u5fae\u7a4d\u5206\u7684\u9748\u9b42\u3001\u4ee5\u53ca\u5404\u89c0\u9ede\u7684\u61c9\u7528\u3002<\/p>\n","protected":false},"author":20,"featured_media":34766,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,148],"tags":[4479,1229,4480,4482,402,4481],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/12\/\u89e3\u8aaa\u5716.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34755"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=34755"}],"version-history":[{"count":8,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34755\/revisions"}],"predecessor-version":[{"id":34767,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34755\/revisions\/34767"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/34766"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=34755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=34755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=34755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}