{"id":25132,"date":"2021-01-18T00:00:25","date_gmt":"2021-01-18T00:00:25","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25132"},"modified":"2024-08-28T19:37:24","modified_gmt":"2024-08-28T19:37:24","slug":"%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/","title":{"rendered":"\u547d\u9898\u903b\u8f91\u8bed\u8a00"},"content":{"rendered":"<h1 style=\"text-align: center;\">\u547d\u9898\u903b\u8f91\u8bed\u8a00<\/h1>\n<h4 style=\"text-align: center;\">\u6458\u8981<\/h4>\n<p style=\"text-align: center;\"><em>\u672c\u7b14\u8bb0\u5ba1\u67e5\u4e86\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4f5c\u4e3a\u4e00\u79cd\u5143\u8bed\u8a00\uff0c\u7528\u4e8e\u4ece\u7531\u4e24\u4e2a\u7b26\u53f7\u7ec4\u6210\u7684\u57fa\u7840\u8bed\u8a00\u4e2d\u83b7\u5f97\u6709\u6548\u7684\u8868\u8fbe\u5f0f\u3002\u89e3\u91ca\u4e86\u53e5\u6cd5\u89c4\u5219\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u7684\u6982\u5ff5\uff0c\u8fd8\u4ecb\u7ecd\u4e86\u8054\u5408\u5426\u5b9a\u3001\u62ec\u53f7\u548c\u91cd\u6392\u7684\u4f7f\u7528\uff0c\u4ee5\u4fbf\u4e8e\u8868\u8fbe\u5f0f\u7684\u9605\u8bfb\u3002\u6b64\u5916\uff0c\u8fd8\u63d0\u5230\u4e86\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3\u3002\u6700\u540e\uff0c\u5c06\u547d\u9898\u903b\u8f91\u8bed\u8a00\u603b\u7ed3\u4e3a\u6570\u5b66\u548c\u903b\u8f91\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\uff0c\u5e76\u63a2\u8ba8\u4e86\u627e\u5230\u201c\u57fa\u7840\u8bed\u8a00\u7684\u57fa\u7840\u8bed\u8a00\u201d\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u7528\u5b83\u91cd\u5efa\u4e00\u5207\u3002<\/em><\/p>\n<h4 style=\"text-align: center;\">\u5b66\u4e60\u76ee\u6807\uff1a<\/h4>\n<p style=\"text-align: justify;\"><em>\u5b8c\u6210\u672c\u90e8\u5206\u540e\uff0c\u671f\u671b\u5b66\u751f\u80fd\u591f\uff1a<\/em><\/p>\n<ol style=\"text-align: justify;\">\n<li><strong>\u7406\u89e3<\/strong>\u5143\u8bed\u8a00\u7684\u6982\u5ff5\u53ca\u5176\u5728\u547d\u9898\u903b\u8f91\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u53e5\u6cd5\u89c4\u5219\u3002<\/li>\n<li><strong>\u4e86\u89e3<\/strong>\u547d\u9898\u53d8\u91cf\u7684\u6982\u5ff5\u53ca\u5176\u5728\u6784\u5efa\u8868\u8fbe\u5f0f\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u8fde\u63a5\u8bcd\u548c\u8054\u5408\u5426\u5b9a\u5728\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4e2d\u7684\u4f7f\u7528\u3002<\/li>\n<li><strong>\u5b66\u4e60<\/strong>\u4f7f\u7528\u62ec\u53f7\u548c\u91cd\u6392\u4ee5\u4fbf\u4e8e\u9605\u8bfb\u8868\u8fbe\u5f0f\u3002<\/li>\n<li><strong>\u4e86\u89e3<\/strong>\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3\u3002<\/li>\n<li><strong>\u603b\u7ed3<\/strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4f5c\u4e3a\u6570\u5b66\u548c\u903b\u8f91\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\u3002<\/li>\n<li><strong>\u601d\u8003<\/strong>\u627e\u5230\u201c\u57fa\u7840\u8bed\u8a00\u7684\u57fa\u7840\u8bed\u8a00\u201d\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u7528\u5b83\u91cd\u5efa\u4e00\u5207\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u6240\u5b66\u6982\u5ff5\u6784\u5efa\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u3002<\/li>\n<li><strong>\u4f7f\u7528<\/strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\u6765\u7406\u89e3\u548c\u89e3\u51b3\u6570\u5b66\u548c\u903b\u8f91\u95ee\u9898\u3002<\/li>\n<\/ol>\n<h4 style=\"text-align: center;\">\u76ee\u5f55<\/h4>\n<p style=\"text-align:center;\">\n<a href=\"#1\"><strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u5b57\u6bcd\u8868\u548c\u7b26\u53f7\u4e32<\/strong><\/a><br \/>\n<a href=\"#2\">\u4ece\u4e00\u4e2a\u7b26\u53f7\u5f00\u59cb<\/a><br \/>\n<a href=\"#3\">\u7136\u540e\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7<\/a><br \/>\n<a href=\"#4\"><strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u53e5\u6cd5<\/strong><\/a><br \/>\n<a href=\"#5\">\u53e5\u6cd5\u5ba1\u67e5\u793a\u4f8b<\/a><br \/>\n<a href=\"#6\"><strong>\u7b26\u53f7\u7ea6\u5b9a<\/strong><\/a><br \/>\n<a href=\"#7\">\u5143\u53d8\u91cf\u4e0e\u8fde\u63a5\u8bcd<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span><\/a><br \/>\n<a href=\"#8\">\u8054\u5408\u5426\u5b9a\u7684\u4f7f\u7528\u793a\u4f8b<\/a><br \/>\n<a href=\"#9\">\u91cd\u6392\u4e0e\u62ec\u53f7<\/a><br \/>\n<a href=\"#10\"><strong>\u6d3e\u751f\u8fde\u63a5\u8bcd<\/strong><\/a><br \/>\n<a href=\"#11\">\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3<\/a><br \/>\n<a href=\"#12\"><strong>\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u603b\u7ed3\u4e0e\u53cd\u601d<\/strong><\/a><br \/>\n<a href=\"#13\">\u7406\u89e3\u4e00\u5207\u80cc\u540e\u7684\u201c\u77e9\u9635\u201d<\/a>\n<\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/WwBKcSXIznA\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u5b57\u6bcd\u8868\u548c\u7b26\u53f7\u4e32<\/h2>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u4ece\u4e00\u4e2a\u7b26\u53f7\u5f00\u59cb<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=WwBKcSXIznA&amp;t=37s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e3a\u4e86\u6784\u5efa\u547d\u9898\u903b\u8f91\u8bed\u8a00<\/strong><\/a>\uff0c\u6211\u4eec\u5c06\u4ece\u6700\u7b80\u5355\u7684\u5b57\u6bcd\u8868\u5f00\u59cb\uff1a\u4e00\u4e2a\u4ec5\u5305\u542b\u4e00\u4e2a\u7b26\u53f7\u7684\u5b57\u6bcd\u8868\u3002\u7b26\u53f7\u7684\u5f62\u72b6\u5e76\u4e0d\u91cd\u8981\uff0c\u91cd\u8981\u7684\u662f\u5b83\u662f\u552f\u4e00\u7684\u3002\u5982\u679c\u6211\u4eec\u4f7f\u7528\u8fd9\u6837\u7684\u5b57\u6bcd\u8868\u8fdb\u884c\u4e66\u5199\uff0c\u552f\u4e00\u533a\u5206\u7b26\u53f7\u4e32\u7684\u56e0\u7d20\u5c31\u662f\u8be5\u7b26\u53f7\u91cd\u590d\u7684\u6b21\u6570\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u5199\u51fa\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u7684\u7b26\u53f7\u4e32\uff0c\u6211\u4eec\u53ea\u80fd\u5199\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e2a\u4e0d\u540c\u7684\u7b26\u53f7\u4e32\u3002\u6b63\u5982\u4f60\u6240\u89c1\uff0c\u8fd9\u4e2a\u5b57\u6bcd\u8868\u975e\u5e38\u6709\u9650\uff0c\u6ca1\u6709\u592a\u591a\u53ef\u4ee5\u8bf4\u7684\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u7136\u540e\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7<\/h3>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u4e3a\u5b57\u6bcd\u8868\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7\uff0c\u4e66\u5199\u4f1a\u6bd4\u4e4b\u524d\u7684\u5b57\u6bcd\u8868\u66f4\u4e30\u5bcc\u3002\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u89c2\u5bdf\u7b26\u53f7\u7684\u6392\u5217\u65b9\u5f0f\uff0c\u4f8b\u5982\uff0c\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u662f\u6211\u4eec\u7684\u7b26\u53f7\uff0c\u6211\u4eec\u53ef\u4ee5\u533a\u5206 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10<\/span><\/span>\u3002\u4e24\u8005\u90fd\u5305\u542b\u76f8\u540c\u7684\u7b26\u53f7\uff0c\u4f46\u987a\u5e8f\u4e0d\u540c\u3002\u5982\u679c\u6211\u4eec\u80fd\u591f\u5199\u51fa\u6700\u957f\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N =1,2,3,\\cdots<\/span><\/span> \u7684\u7b26\u53f7\u4e32\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5199\u51fa <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^1=2<\/span><\/span> \u4e2a\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u7684\u7b26\u53f7\u4e32\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^2=4<\/span><\/span> \u4e2a\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">2<\/span> \u7684\u7b26\u53f7\u4e32\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^3=8<\/span><\/span> \u4e2a\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">3<\/span> \u7684\u7b26\u53f7\u4e32\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u4e00\u822c\u6765\u8bf4\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> 2^N<\/span><\/span> \u4e2a\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u7684\u4e0d\u540c\u7b26\u53f7\u4e32\u3002<\/p>\n<p style=\"text-align: justify;\"><strong>\u7ec3\u4e60\uff1a<\/strong>\u5728\u7eb8\u4e0a\u5199\u4e0b\u6240\u6709\u53ef\u80fd\u7684\u4e0d\u540c\u7b26\u53f7\u4e32\uff0c\u957f\u5ea6\u4ece <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u5230 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u4e0d\u7b49\u3002\u603b\u5171\u53ef\u4ee5\u5199\u51fa\u591a\u5c11\u4e2a\u7b26\u53f7\u4e32\uff1f<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #0000aa;\"><strong>\u89e3\u7b54\uff1a<\/strong><\/span><br \/>\n\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S_N<\/span><\/span> \u662f\u6240\u6709\u7b26\u53f7\u4e32\u7684\u603b\u548c\uff0c\u957f\u5ea6\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1, 2, 3, <\/span><\/span> \u7b49\u7b49\u76f4\u5230 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle S_N=2^1 + 2^2 + \\cdots +2^{N-1} + 2^N <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5c06\u4e0a\u5f0f\u4e58\u4ee5 2\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 2 S_N=2^2 + 2^3 + \\cdots + 2^N + 2^{N+1} <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle S_N=2 S_N - S_N = 2^N-1 <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u5728\u7eb8\u4e0a\u5199\u4e0b\u7684\u603b\u7b26\u53f7\u4e32\u6570\u91cf\u5c06\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^N-1<\/span><\/span>\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u53e5\u6cd5<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=WwBKcSXIznA&amp;t=295s\" target=\"_blank\" rel=\"noopener\"><strong>\u6211\u4eec\u5df2\u7ecf\u770b\u5230\uff0c\u4f7f\u7528\u4e24\u4e2a\u7b26\u53f7\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7b26\u53f7\u4e32\u7684\u957f\u5ea6\u548c\u7b26\u53f7\u7684\u6392\u5217\u987a\u5e8f\u6765\u533a\u5206\u5b83\u4eec\u3002<\/strong><\/a> \u8fd9\u5f88\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u6211\u4eec\u4e3a\u6784\u5efa\u7684\u5b57\u6bcd\u8868\u5b9a\u4e49\u53e5\u6cd5\u3002\u53e5\u6cd5\u662f\u4e00\u7ec4\u89c4\u5219\uff0c\u5c06\u7b26\u53f7\u4e32\u5206\u4e3a\u4e24\u7c7b\uff1a\u8868\u8fbe\u5f0f\u548c\u975e\u8868\u8fbe\u5f0f\u3002\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{L}_2<\/span><\/span> \u662f\u53ef\u4ee5\u7528\u7b26\u53f7 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u6784\u5efa\u7684\u6240\u6709\u7b26\u53f7\u4e32\u7684\u96c6\u5408\uff0c\u90a3\u4e48 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{L}_2<\/span><\/span> \u7684\u53e5\u6cd5\u662f\u4e00\u4e2a\u5b50\u96c6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2\\subset\\mathcal{L}_2<\/span><\/span>\u3002<\/p>\n<p style=\"text-align: justify;\">\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u9012\u5f52\u89c4\u5219\u5b9a\u4e49\u96c6\u5408 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span>\uff1a<\/p>\n<ol>\n<li style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00, 11 \\in \\mathcal{SL}_2<\/span><\/span><\/li>\n<li style=\"text-align: justify;\">\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\beta \\in \\mathcal{SL}_2<\/span><\/span>\uff0c\u5219 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01\\alpha\\beta \\in \\mathcal{SL}_2<\/span><\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e24\u4e2a\u89c4\u5219\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\uff0c\u5e76\u9a8c\u8bc1\u7ed9\u5b9a\u7684\u7b26\u53f7\u4e32\u662f\u5426\u4e3a\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\u3002\u8bed\u8a00\u662f\u5177\u6709\u76f8\u5173\u53e5\u6cd5\u7684\u5b57\u6bcd\u8868\u3002\u6211\u4eec\u5c06\u8fd9\u91cc\u4ecb\u7ecd\u7684\u8bed\u8a00\u547d\u540d\u4e3a<em>\u201c\u4e8c\u7b26\u53f7\u57fa\u7840\u8bed\u8a00\u201d<\/em>\uff0c\u6216 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span>\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u53e5\u6cd5\u5ba1\u67e5\u793a\u4f8b<\/h3>\n<p style=\"text-align: justify;\">\u4e3a\u4e86\u66f4\u5bb9\u6613\u7406\u89e3\u8fd9\u4e9b\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u6765\u770b\u4ee5\u4e0b\u793a\u4f8b\uff1a<\/p>\n<p style=\"text-align: justify;\"><strong>\u793a\u4f8b\uff1a<\/strong> \u9274\u4e8e <span style=\"color: #FF4500;\"><span class=\"katex-eq\" data-katex-display=\"false\">0000<\/span><\/span> \u548c <span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">1111<\/span><\/span> \u5305\u542b\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u4e2d\uff0c\u56e0\u6b64 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00 00 01 00<\/span><\/span><\/span><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">11 01 11<\/span><\/span><\/span><span style=\"color: #FF4500;\"><span class=\"katex-eq\" data-katex-display=\"false\">0000<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span><span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">1111<\/span><\/span><span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">1111<\/span><\/span> \u90fd\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u4e2d\uff1b\u56e0\u6b64\uff0c\u5b83\u4eec\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u6211\u4eec\u521a\u521a\u4ecb\u7ecd\u7684\u89c4\u5219\u6765\u8bc1\u660e\u3002<br \/>\n<\/span><\/p>\n<p>\u793a\u4f8b\u7ed3\u675f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\blacksquare<\/span><\/span><\/p>\n<p><strong>\u7ec3\u4e60\uff1a<\/strong> \u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u4e86\u5982\u4f55\u4ece\u5176\u4ed6\u4e24\u4e2a\u57fa\u672c\u8868\u8fbe\u5f0f\u6784\u5efa\u8868\u8fbe\u5f0f\u3002\u8fd9\u5e76\u4e0d\u590d\u6742\uff1b\u7136\u800c\uff0c\u9006\u5411\u8fc7\u7a0b\uff0c\u5373\u8bc1\u660e\u67d0\u4e2a\u8868\u8fbe\u5f0f\u662f\u5426\u4e3a\u8868\u8fbe\u5f0f\uff0c\u53ef\u80fd\u4f1a\u66f4\u5177\u6311\u6218\u6027\u3002<\/p>\n<p style=\"text-align: justify;\"><span style=\"\">\u8bf7\u6839\u636e\u53e5\u6cd5\u89c4\u5219\u786e\u5b9a\u4ee5\u4e0b\u7b26\u53f7\u4e32\u662f\u5426\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\uff1a<br \/>\n<\/span><\/p>\n<ol>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{}012100<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">101100<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{}0100010000<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0101000011<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{}01010000010000<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01010010000100101000011<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><span style=\"color: #0000aa;\"><strong>\u89e3\u7b54\uff1a<\/strong><\/span><br \/>\n\u5728\u67e5\u770b\u89e3\u7b54\u4e4b\u524d\uff0c\u6211\u5efa\u8bae\u4f60\u5148\u81ea\u5df1\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u7136\u540e\u518d\u6bd4\u8f83\u7ed3\u679c\u3002\u5982\u679c\u4f60\u5df2\u7ecf\u5b8c\u6210\u4e86\uff0c\u90a3\u4e48\u7ee7\u7eed\ud83d\udc4d<\/p>\n<ol>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span><span class=\"katex-eq\" data-katex-display=\"false\">2<\/span><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">100<\/span><\/span>.<\/p>\n<p style=\"text-align: justify;\">\u6b63\u5982\u6211\u4eec\u6240\u89c1\uff0c\u5b83\u5305\u542b\u7b26\u53f7 <span class=\"katex-eq\" data-katex-display=\"false\">2<\/span>\uff0c\u8be5\u7b26\u53f7\u4e0d\u5305\u542b\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{L}_2<\/span><\/span> \u4e2d\uff1b\u56e0\u6b64\uff0c\u6b64\u7b26\u53f7\u4e32\u4e0d\u80fd\u5305\u542b\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u4e2d\uff0c\u56e0\u6b64\u4e0d\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10<\/span><\/span><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1100<\/span><\/span>.<\/p>\n<p style=\"text-align: justify;\">\u8fd9\u91cc\u53ef\u4ee5\u770b\u51fa\uff0c\u8fd9\u4e2a\u7b26\u53f7\u4e32\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10<\/span><\/span> \u5f00\u5934\u3002\u6839\u636e\u53e5\u6cd5\u89c4\u5219\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u65ad\u51fa\uff0c\u6240\u6709\u957f\u5ea6\u8d85\u8fc7 2 \u7684\u7b26\u53f7\u4e32\u5fc5\u987b\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span> \u5f00\u5934\uff0c\u56e0\u6b64\u5b83\u4e0d\u80fd\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0100010000<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u8fd9\u4e2a\u7b26\u53f7\u4e32\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span> \u5f00\u5934\uff0c\u56e0\u6b64\u901a\u8fc7\u4e86\u7b2c\u4e00\u4e2a\u6d4b\u8bd5\u3002\u4e3a\u4e86\u4f7f\u5176\u6210\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{L}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\uff0c\u6709\u5fc5\u8981\u5c06\u84dd\u8272\u6807\u8bb0\u90e8\u5206\u552f\u4e00\u5730\u5206\u89e3\u4e3a\u4e24\u4e2a\u8868\u8fbe\u5f0f\u3002<span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00010000<\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"\">\u5982\u679c\u5373\u4f7f\u9075\u5faa\u53e5\u6cd5\u89c4\u5219\uff0c\u5206\u89e3\u4ecd\u7136\u4e0d\u662f\u552f\u4e00\u7684\uff0c\u90a3\u4e48\u5b9a\u4e49\u7684\u53e5\u6cd5\u662f\u6a21\u68f1\u4e24\u53ef\u7684\uff0c\u56e0\u6b64\u5fc5\u987b\u8fdb\u884c\u4fee\u6b63\u3002<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\">\u5206\u6790\u84dd\u8272\u90e8\u5206\uff0c\u53ef\u80fd\u7684\u5206\u89e3\u5982\u4e0b\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0010000<\/span><\/span><\/span><\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010000<\/span><\/span><\/span><\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10000<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0001<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0000<\/span><\/span><\/span><\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00010<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000<\/span><\/span><\/span><\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000100<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0001000<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/span><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u5728\u8fd9\u90e8\u5206\uff0c\u6211\u4eec\u9700\u8981\u6ce8\u610f\uff0c\u5982\u679c\u91d1\u8272\u90e8\u5206\u4e0d\u662f <span class=\"katex-eq\" data-katex-display=\"false\">0000<\/span> 0 <span class=\"katex-eq\" data-katex-display=\"false\">1111<\/span>\uff0c\u90a3\u4e48\u76f8\u5e94\u7684\u84dd\u8272\u90e8\u5206\u5fc5\u987b\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span> \u5f00\u5934\uff0c\u4ee5\u786e\u4fdd\u6574\u4e2a\u7b26\u53f7\u4e32\u662f\u8868\u8fbe\u5f0f\uff0c\u56e0\u6b64\u53ef\u4ee5\u8fdb\u884c\u4ee5\u4e0b\u6392\u9664<\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{}0010000<\/span><\/span><\/span>\u274c<\/td>\n<td><span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><span style=\"color: #007ACC ;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010000<\/span><\/span>\u2705<\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{}10000<\/span><\/span><\/span>\u274c<\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0001<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0000<\/span><\/span><\/span>\u274c<\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00010<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000<\/span><\/span><\/span>\u274c<\/td>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">000100<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><\/span>\u274c<\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #DAA520 ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0001000<\/span><\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/span>\u274c<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u552f\u4e00\u901a\u8fc7\u5206\u6790\u7684\u5206\u89e3\u662f <span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010000<\/span><\/span><\/span>\uff0c\u5176\u4e2d\u91d1\u8272\u90e8\u5206\u662f\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u84dd\u8272\u90e8\u5206\u53ef\u4ee5\u552f\u4e00\u4e14\u7b26\u5408\u53e5\u6cd5\u5730\u5206\u89e3\u3002\u6700\u540e\uff0c\u7b26\u53f7\u4e32 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0100010000<\/span><\/span> \u5141\u8bb8\u552f\u4e00\u4e14\u7b26\u5408\u53e5\u6cd5\u7684\u5206\u89e3\uff0c\u5373 <span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">00<\/span><\/span><span style=\"color: #007ACC ;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010000<\/span><\/span>\uff0c\u56e0\u6b64\u5b83\u662f\u8bed\u8a00 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0101000011<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5bf9\u4e8e\u8fd9\u4e2a\u7b26\u53f7\u4e32\uff0c\u6211\u4eec\u53ef\u4ee5\u505a\u4ee5\u4e0b\u5206\u89e3\uff0c\u7528\u989c\u8272\u6807\u8bb0\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span><span style=\"color: #007ACC ;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010000<\/span><\/span><\/span><span style=\"color: #DAA520 ;\"><span class=\"katex-eq\" data-katex-display=\"false\">1111<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u6839\u636e\u53e5\u6cd5\u89c4\u5219\uff0c\u957f\u5ea6\u8d85\u8fc7 2 \u7684\u7b26\u53f7\u4e32\u5fc5\u987b\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span> \u5f00\u5934\uff0c\u7136\u540e\u5fc5\u987b\u8ddf\u968f\u4e24\u4e2a\u8868\u8fbe\u5f0f\uff0c\u5206\u522b\u7528\u84dd\u8272\u548c\u91d1\u8272\u6807\u8bb0\u3002\u5f88\u5bb9\u6613\u770b\u51fa\uff0c\u8fd9\u4e2a\u5206\u89e3\u662f\u552f\u4e00\u7684\uff0c\u56e0\u4e3a\u5982\u679c\u84dd\u8272\u6216\u91d1\u8272\u90e8\u5206\u7684\u957f\u5ea6\u53d1\u751f\u53d8\u5316\uff0c\u65e0\u8bba\u662f\u4ec0\u4e48\u53d8\u5316\uff0c\u4e24\u90e8\u5206\u90fd\u4e0d\u4f1a\u540c\u65f6\u662f\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01010000010000<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u4ece\u53f3\u5411\u5de6\u68c0\u67e5\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u4ee5\u4e0b\u5206\u89e3\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\underbrace{01\\underbrace{01\\overbrace{00}\\overbrace{00}}_{{\u8868\u8fbe\u5f0f}}\\underbrace{01\\overbrace{00}\\overbrace{00}}_{{\u8868\u8fbe\u5f0f}}}_{{\u8868\u8fbe\u5f0f}}<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01010010000100101000011<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u654f\u9510\u7684\u773c\u775b\u4f1a\u6ce8\u610f\u5230\uff0c\u8fd9\u4e2a\u7b26\u53f7\u4e32\u7684\u957f\u5ea6\u4e3a 23\uff0c\u800c\u6839\u636e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{L}_2<\/span><\/span> \u7684\u53e5\u6cd5\u89c4\u5219\uff0c\u4e0d\u53ef\u80fd\u6784\u5efa\u957f\u5ea6\u4e3a\u5947\u6570\u7684\u7b26\u53f7\u4e32\uff0c\u56e0\u4e3a\u5b83\u901a\u8fc7\u5e76\u7f6e\u957f\u5ea6\u4e3a\u5076\u6570\u7684\u7b26\u53f7\u4e32\u6784\u5efa\u8868\u8fbe\u5f0f\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u7684\u6240\u6709\u7b26\u53f7\u4e32\u90fd\u5177\u6709\u5076\u6570\u957f\u5ea6\uff0c\u56e0\u6b64 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01010010000100101000011<\/span><\/span> \u4e0d\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u7ec3\u4e60\u7ed3\u675f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\blacksquare<\/span><\/span><\/p>\n<figure id=\"attachment_25115\" aria-describedby=\"caption-attachment-25115\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos.jpg\" alt=\"\u4e00\u5757\u89e3\u7801\u7b26\u53f7\u7684\u77f3\u677f\" width=\"1081\" height=\"399\" class=\"size-full wp-image-25115 lazyload\" \/><figcaption id=\"caption-attachment-25115\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos.jpg\" alt=\"\u4e00\u5757\u89e3\u7801\u7b26\u53f7\u7684\u77f3\u677f\" width=\"1081\" height=\"399\" class=\"size-full wp-image-25115 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos.jpg 1081w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos-300x111.jpg 300w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos-1024x378.jpg 1024w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/simbolos-768x283.jpg 768w\" sizes=\"(max-width: 1081px) 100vw, 1081px\" \/><\/noscript><\/figcaption><\/figure>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u7b26\u53f7\u7ea6\u5b9a<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=WwBKcSXIznA&amp;t=918s\" target=\"_blank\" rel=\"noopener\"><strong>\u4f7f\u7528 0 \u548c 1 \u53ef\u80fd\u4f1a\u4f7f\u6211\u4eec\u611f\u5230\u56f0\u60d1<\/strong><\/a> \u5e76\u5bfc\u81f4\u6211\u4eec\u72af\u9519\u8bef\u3002\u4e3a\u4e86\u8ba9\u8fc7\u7a0b\u66f4\u7b26\u5408\u4eba\u7c7b\u7684\u7406\u89e3\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7b26\u53f7\u7ea6\u5b9a\u548c\u4e00\u4e9b\u5143\u7b26\u53f7\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u5143\u53d8\u91cf\u548c\u8fde\u8bcd <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=WwBKcSXIznA&amp;t=950s\" target=\"_blank\" rel=\"noopener\"><strong>\u5143\u7b26\u53f7\u662f\u7528\u4e8e\u8868\u793a\u76ee\u6807\u8bed\u8a00\u7b26\u53f7\u4e32\u7684\u7b26\u53f7\u3002<\/strong><\/a> \u4f8b\u5982\uff0c\u5f53\u5b9a\u4e49 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u7684\u53e5\u6cd5\u65f6\uff0c\u4f7f\u7528\u4e86\u7b26\u53f7 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u6765\u8868\u793a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002\u8fd9\u4e9b\u7b26\u53f7\u88ab\u79f0\u4e3a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u53d8\u91cf\uff1a<\/strong> \u5143\u7b26\u53f7\uff0c\u5f53\u5b83\u4eec\u5168\u90e8\u88ab\u8bed\u8a00\u8868\u8fbe\u5f0f\u53d6\u4ee3\u65f6\uff0c\u901a\u8fc7\u53e5\u6cd5\u751f\u6210\u53e6\u4e00\u4e2a\u8bed\u8a00\u8868\u8fbe\u5f0f\uff0c\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u8ba8\u8bba\u7684\u5173\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u5143\u7d20\u7684\u7b2c\u4e8c\u6761\u89c4\u5219\u6240\u793a\uff1a<\/p>\n<p style=\"text-align: center;\">\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta \\in \\mathcal{SL}_2<\/span><\/span>\uff0c\u5219 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01\\alpha\\beta \\in\\mathcal{SL}_2<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u8fd9\u4e9b\u5143\u53d8\u91cf\u88ab\u79f0\u4e3a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u8868\u8fbe\u5f0f\u3002<\/strong><\/p>\n<p style=\"text-align: justify;\">\u4e3a\u4e86\u7b80\u5316\u6211\u4eec\u7684\u5199\u4f5c\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u5143\u7b26\u53f7 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span> \u6765\u8868\u793a\u7b26\u53f7\u4e32 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">01<\/span><\/span>\u3002\u8fd9\u4e2a\u5143\u7b26\u53f7\u662f\u6211\u4eec\u6240\u8c13\u7684 <strong>\u8fde\u8bcd<\/strong>\uff0c\u7531\u4e8e\u8bed\u4e49\u539f\u56e0\uff0c\u5b83\u88ab\u79f0\u4e3a <strong>\u8054\u5408\u5426\u5b9a<\/strong>\u3002<\/p>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u9012\u5f52\u89c4\u5219\uff0c\u4ee5\u5143\u8bed\u8a00\u8868\u8fbe <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{SL}_2<\/span><\/span> \u7684\u53e5\u6cd5\uff1a<\/p>\n<ol>\n<li>\n<p style=\"text-align: justify;\">\u6240\u6709 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u53d8\u91cf\u90fd\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\">\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u53d8\u91cf\uff0c\u90a3\u4e48 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\beta<\/span><\/span> \u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u5143\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e9b\u89c4\u5219\uff0c\u6211\u4eec\u53ef\u4ee5\u7f16\u5199\u5143\u8868\u8fbe\u5f0f\uff0c\u5f53\u5b83\u4eec\u7684\u6240\u6709\u5143\u53d8\u91cf\u90fd\u88ab\u8868\u8fbe\u5f0f\u548c <strong>\u8fde\u8bcd<\/strong> \u4ee5 0 \u548c 1 \u7684\u5f62\u5f0f\u8868\u793a\u65f6\uff0c\u4fbf\u751f\u6210\u4e86 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u6bcf\u4e2a\u5143\u8868\u8fbe\u5f0f\u90fd\u4ee3\u8868\u4e86\u4e00\u4e2a\u65e0\u9650\u7684\u8868\u8fbe\u5f0f\u5bb6\u65cf\uff1a\u53ef\u4ee5\u901a\u8fc7\u8be5\u7ed3\u6784\u8868\u793a\u7684\u6240\u6709 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{B}_2<\/span><\/span> \u8868\u8fbe\u5f0f\u7684\u96c6\u5408\u3002\u8fd9\u6b63\u662f\u62e5\u6709\u5f62\u5f0f\u8bed\u8a00\u7684\u542b\u4e49\u3002<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h4>\u8054\u5408\u5426\u5b9a\u7684\u4f7f\u7528\u793a\u4f8b<\/h4>\n<p style=\"text-align: justify;\"><strong>\u793a\u4f8b\uff1a<\/strong> <span style=\"\"> \u4ece\u5143\u8868\u8fbe\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow\\beta\\gamma<\/span><\/span> \u53ef\u4ee5\u901a\u8fc7\u66ff\u6362\u5f97\u5230\u4ee5\u4e0b\u8868\u8fbe\u5f0f\uff1a<br \/>\n<\/span><\/p>\n<ol>\n<li>\n<p style=\"text-align: justify;\">\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha := 00<\/span><\/span>\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta := 011100<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma := 010011<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5f97\u5230\u8868\u8fbe\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010001011100010011<\/span><\/span><\/p>\n<\/li>\n<li>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha := 011100<\/span><\/span>\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta := 0111011100<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma := 0111010011<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u751f\u6210\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">010111000101110111000111010011<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u5143\u8868\u8fbe\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow\\beta\\gamma<\/span><\/span> \u4e0d\u4ec5\u6bd4\u4efb\u4f55\u5176\u4ed6\u7b26\u5408\u5176\u5f62\u5f0f\u7684\u8868\u8fbe\u5f0f\u66f4\u5bb9\u6613\u7406\u89e3\uff0c\u800c\u4e14\u5b83\u8fd8\u4ee3\u8868\u4e86\u6240\u6709\u53ef\u4ee5\u901a\u8fc7\u66ff\u6362\u5176\u5143\u53d8\u91cf\u5f97\u5230\u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<p>\u793a\u4f8b\u7ed3\u675f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\blacksquare<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5f53\u66ff\u6362\u5143\u53d8\u91cf\u65f6\uff0c\u9700\u8981\u5728\u6240\u6709\u51fa\u73b0\u7684\u5730\u65b9\u66ff\u6362\u3002<\/p>\n<p style=\"text-align: justify;\"><strong>\u793a\u4f8b\uff1a<\/strong> <span style=\"\"> \u8003\u8651\u5143\u8868\u8fbe\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\downarrow\\alpha\\beta\\downarrow\\alpha\\gamma<\/span><\/span><br \/>\n<\/span><\/p>\n<ol>\n<li>\u5982\u679c\u6211\u4eec\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha:=11<\/span><\/span>\uff0c\u6211\u4eec\u5f97\u5230\uff1a\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\downarrow 11\\beta\\downarrow 11\\gamma<\/span><\/span><\/p>\n<\/li>\n<li>\u5982\u679c\u6211\u4eec\u73b0\u5728\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta:=011100<\/span><\/span>\uff0c\u7ed3\u679c\u5c06\u662f\uff1a\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\downarrow 11011100\\downarrow 11\\gamma<\/span><\/span><\/p>\n<\/li>\n<li>\u5982\u679c\u6211\u4eec\u73b0\u5728\u5c06 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma:=011111<\/span><\/span> \u8fdb\u884c\u66ff\u6362\uff0c\u5f97\u5230\uff1a\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\downarrow 11011100\\downarrow 11011111<\/span><\/span><\/p>\n<\/li>\n<li>\u6700\u540e\uff0c\u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow:=01<\/span><\/span>\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u8868\u8fbe\u5f0f\uff1a\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0101110111000111011111<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p>\u793a\u4f8b\u7ed3\u675f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\blacksquare<\/span><\/span><\/p>\n<p><a name=\"9\"><\/a><\/p>\n<h3>\u91cd\u65b0\u6392\u5e8f\u4e0e\u62ec\u53f7<\/h3>\n<p style=\"text-align: justify;\">\u9a8c\u8bc1\u8fd9\u662f\u5426\u662f\u4e00\u4e2a\u5143\u8868\u8fbe\u5f0f\u5e76\u4e0d\u662f\u7279\u522b\u56f0\u96be\uff0c\u4f46\u9700\u8981\u65f6\u523b\u5173\u6ce8\u5143\u7b26\u53f7\u7684\u6570\u91cf\u548c\u8fde\u8bcd <span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span> \u7684\u8303\u56f4\u3002\u968f\u7740\u5143\u8868\u8fbe\u5f0f\u957f\u5ea6\u7684\u589e\u52a0\uff0c\u8fd9\u79cd\u56f0\u96be\u4f1a\u8fc5\u901f\u589e\u52a0\u3002\u56e0\u6b64\uff0c\u6709\u4e00\u4e2a\u5408\u7406\u7684\u95ee\u9898\uff1a\u662f\u5426\u5b58\u5728\u4e00\u79cd\u66f4\u5bb9\u6613\u9a8c\u8bc1\u8fd9\u4e9b\u5185\u5bb9\u7684\u65b9\u6cd5\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff1b\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u62ec\u53f7\u548c\u9002\u5f53\u7684\u91cd\u65b0\u6392\u5e8f\u6765\u66f4\u597d\u5730\u9002\u5e94\u6211\u4eec\u81ea\u7136\u7684\u5206\u7ec4\u65b9\u5f0f\u3002\u4e3a\u4e86\u8bf4\u660e\u8fd9\u4e00\u70b9\uff0c\u8ba9\u6211\u4eec\u6765\u5ba1\u67e5\u4ee5\u4e0b\u5143\u8868\u8fbe\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow\\downarrow\\alpha\\beta\\alpha<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5c3d\u7ba1\u786e\u8ba4\u8fd9\u662f\u5426\u662f\u4e00\u4e2a\u5143\u8868\u8fbe\u5f0f\u5e76\u4e0d\u7279\u522b\u56f0\u96be\uff0c\u4f46\u6211\u4eec\u65e0\u6cd5\u5728\u4e0d\u6570\u7b26\u53f7\u7684\u60c5\u51b5\u4e0b\u8fdb\u884c\u64cd\u4f5c\uff0c\u800c\u4e14\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u5931\u53bb\u5bf9\u7b26\u53f7\u6570\u91cf\u7684\u63a7\u5236\uff0c\u800c\u968f\u7740\u5143\u8868\u8fbe\u5f0f\u957f\u5ea6\u7684\u589e\u52a0\uff0c\u8fd9\u79cd\u98ce\u9669\u4e5f\u4f1a\u8fc5\u901f\u589e\u52a0\u3002\u662f\u5426\u6709\u66f4\u4fbf\u4e8e\u9605\u8bfb\u7684\u65b9\u5f0f\u6765\u8868\u793a\u76f8\u540c\u5185\u5bb9\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff0c\u8fd9\u79cd\u65b9\u6cd5\u7b26\u5408\u6211\u4eec\u81ea\u7136\u7684\u5206\u7ec4\u65b9\u5f0f\u3002\u4e3a\u6b64\uff0c\u5f15\u5165\u62ec\u53f7\u548c\u91cd\u65b0\u6392\u5e8f\u7684\u7b26\u53f7\u7ea6\u5b9a\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\beta:=(\\alpha\\downarrow\\beta)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><strong>\u793a\u4f8b\uff1a<\/strong> \u8ba9\u6211\u4eec\u8003\u8651\u5143\u8868\u8fbe\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow\\downarrow\\beta\\gamma\\delta<\/span><\/span>\u3002\u5982\u679c\u6211\u4eec\u5e94\u7528\u62ec\u53f7\u548c\u91cd\u65b0\u6392\u5e8f\u7684\u7ea6\u5b9a\uff0c\u90a3\u4e48\u5b83\u5c06\u6309\u5982\u4e0b\u65b9\u5f0f\u8f6c\u53d8\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow<\/span><\/span><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\beta\\gamma<\/span><\/span><\/span><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha\\downarrow<\/span><\/span><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\beta\\downarrow \\gamma)<\/span><\/span><\/span><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha<\/span><\/span><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow(\\beta\\downarrow \\gamma)\\delta<\/span><\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha<\/span><\/span><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((\\beta\\downarrow \\gamma)\\downarrow\\delta)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow\\alpha((\\beta\\downarrow \\gamma)\\downarrow\\delta)<\/span><\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span style=\"color: #FF4500;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\downarrow((\\beta\\downarrow \\gamma)\\downarrow\\delta))<\/span><\/span><\/span> \u2705<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u6700\u540e\u7684\u8fd9\u4e2a\u5143\u8868\u8fbe\u5f0f\u6bd4\u539f\u59cb\u8868\u8fbe\u5f0f\u66f4\u5bb9\u6613\u9605\u8bfb\u548c\u68c0\u67e5\uff0c\u56e0\u4e3a\u6bcf\u4e2a\u62ec\u53f7\u5757\u90fd\u662f\u7531\u6613\u4e8e\u533a\u5206\u7684\u5143\u7d20\u7ec4\u6210\u7684\u5143\u8868\u8fbe\u5f0f\uff1a\u4e00\u4e2a\u5728\u4e2d\u5fc3\u7684\u8054\u5408\u5426\u5b9a\u7b26\u53f7\u548c\u4e24\u8fb9\u7684\u5143\u8868\u8fbe\u5f0f\u3002<\/p>\n<p>\u793a\u4f8b\u7ed3\u675f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\blacksquare<\/span><\/span><\/p>\n<p><a name=\"10\"><\/a><\/p>\n<h3>\u884d\u751f\u8fde\u8bcd<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=WwBKcSXIznA&amp;t=1478s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u903b\u8f91\u548c\u6570\u5b66\u4e2d\uff0c<\/strong><\/a>\u5b58\u5728\u67d0\u4e9b\u8fde\u8bcd\u7ec4\u5408\u88ab\u9891\u7e41\u4f7f\u7528\u3002\u4e3a\u6b64\uff0c\u4e3a\u4e86\u4f7f\u4e66\u5199\u66f4\u52a0\u65b9\u4fbf\uff08\u5bf9\u4e8e\u4eba\u7c7b\u800c\u8a00\uff09\uff0c\u901a\u8fc7\u4ee5\u4e0b\u7b26\u53f7\u7ea6\u5b9a\u5f15\u5165\u4e86\u884d\u751f\u8fde\u8bcd\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>\u5426\u5b9a\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg \\alpha<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\downarrow\\alpha)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>\u6216\u8fd0\u7b97\uff08\u5305\u542b\u6027\u201c\u6216\u201d\uff09\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha\\downarrow\\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>\u4e0e\u8fd0\u7b97\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg\\alpha\\vee \\neg\\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>\u8574\u542b\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\neg\\alpha\\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>\u53cc\u5411\u8574\u542b\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\leftrightarrow \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((\\alpha\\rightarrow \\beta)\\wedge(\\beta \\rightarrow \\alpha))<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>\u5f02\u6216\uff1a<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\veebar \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha\\leftrightarrow \\beta)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u6211\u4eec\u5728<strong>\u4e24\u4e2a\u7b26\u53f7\u57fa\u7840\u8bed\u8a00<\/strong>\u4e4b\u4e0a\u6784\u5efa\u7684\u8fd9\u79cd\u5143\u8bed\u8a00\u5c31\u662f\u6240\u8c13\u7684<strong>\u547d\u9898\u903b\u8f91\u7684\u96f6\u9636\u8bed\u8a00<\/strong>\u3002\u901a\u8fc7\u8fd9\u79cd\u8bed\u8a00\uff0c\u53ef\u4ee5\u7cbe\u786e\u5730\u4e14\u65e0\u6b67\u4e49\u5730\u8868\u793a\u547d\u9898\u903b\u8f91\u7684\u6240\u6709\u8868\u8fbe\u5f0f\u3002<\/p>\n<p><a name=\"11\"><\/a><\/p>\n<h2>\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3<\/h2>\n<p style=\"text-align: justify;\">\u867d\u7136\u903b\u8f91\u63a8\u7406\u4e0d\u4e00\u5b9a\u9700\u8981\u53d1\u97f3\uff0c\u4f46\u6211\u4eec\u9700\u8981\u8ba4\u8bc6\u5230\u6211\u4eec\u7684\u4ea4\u6d41\u4e0d\u4ec5\u4ec5\u4f9d\u8d56\u4e8e\u4e66\u9762\u7b26\u53f7\uff0c\u6211\u4eec\u4e5f\u503e\u5411\u4e8e\u5728\u81ea\u7136\u8bed\u8a00\u4e2d\u5c06\u4e8b\u7269\u53d1\u97f3\u3002\u56e0\u6b64\uff0c\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\u6709\u5176\u53d1\u97f3\uff0c\u80fd\u591f\u5524\u8d77\u7c7b\u4f3c\u4e8e\u547d\u9898\u903b\u8f91\u4e2d\u5176\u5bf9\u5e94\u8868\u8fbe\u5f0f\u6240\u8868\u8fbe\u7684\u60f3\u6cd5\u3002\u4ee5\u4e0b\u662f\u8fd9\u4e9b\u53d1\u97f3\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\downarrow \\beta)<\/span><\/span> <\/td>\n<td>\u65e2\u4e0d<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u4e5f\u4e0d<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg \\alpha<\/span><\/span> <\/td>\n<td>\u5426\u5b9a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta)<\/span><\/span> <\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u6216<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge \\beta)<\/span><\/span> <\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u4e0e<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta)<\/span><\/span> <\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u8574\u542b<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\leftrightarrow \\beta)<\/span><\/span> <\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u5f53\u4e14\u4ec5\u5f53<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\veebar \\beta)<\/span><\/span> <\/td>\n<td>\u8981\u4e48<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\uff0c\u8981\u4e48<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span>\uff0c\u4f46\u4e0d\u662f\u4e24\u8005<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"12\"><\/a><\/p>\n<h2>\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u603b\u7ed3\u4e0e\u53cd\u601d<\/h2>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u6700\u540e\u8fd9\u90e8\u5206\uff0c\u6211\u4eec\u5b8c\u6210\u4e86\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u6784\u5efa\uff0c\u53ef\u4ee5\u5c06\u5176\u603b\u7ed3\u4e3a\u4e00\u79cd\u5143\u8bed\u8a00\uff0c\u80fd\u591f\u5728\u4e24\u4e2a\u7b26\u53f7\u7684\u57fa\u7840\u8bed\u8a00\u4e2d\u5f97\u5230\u6709\u6548\u8868\u8fbe\u3002\u547d\u9898\u903b\u8f91\u8bed\u8a00\u662f\u4e00\u79cd\u5f62\u5f0f\u8bed\u8a00\uff0c\u56e0\u4e3a\u5b83\u5b9a\u4e49\u4e86\u57fa\u7840\u8bed\u8a00\u8868\u8fbe\u5f0f\u7684\u7ed3\u6784\uff08\u6216\u5f62\u5f0f\uff09\uff0c\u5e76\u4e14\u5176\u6bcf\u4e2a\u8868\u8fbe\u5f0f\u51b3\u5b9a\u4e86\u57fa\u7840\u8bed\u8a00\u4e2d\u65e0\u9650\u591a\u7684\u8868\u8fbe\u5f0f\u5f62\u5f0f\u3002\u6b63\u5982\u524d\u9762\u63d0\u5230\u7684\uff0c\u5f62\u5f0f\u8bed\u8a00\u7684\u8bed\u6cd5\u6781\u5176\u4e25\u683c\uff0c\u4f46\u4f5c\u4e3a\u4ea4\u6362\uff0c\u5b83\u5177\u6709\u7cbe\u786e\u6027\u548c\u65e0\u6b67\u4e49\u6027\u3002<\/p>\n<p><a name=\"13\"><\/a><\/p>\n<h3>\u7406\u89e3\u4e00\u5207\u4e8b\u7269\u7684 Matrix \u80cc\u540e\u7684 Matrix<\/h3>\n<p style=\"text-align: justify;\"><span style=\"\">\u6700\u540e\u4e00\u4ef6\u4e8b\u3002\u547d\u9898\u903b\u8f91\u548c\u6570\u5b66\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4f9d\u8d56\u4e8e\u547d\u9898\u903b\u8f91\uff0c\u800c\u547d\u9898\u903b\u8f91\u662f\u5efa\u7acb\u5728\u7531 0 \u548c 1 \u7ec4\u6210\u7684\u57fa\u7840\u8bed\u8a00\u4e4b\u4e0a\u7684\u3002\u8fd9\u662f\u5426\u610f\u5473\u7740\u6211\u4eec\u5df2\u7ecf\u89e6\u53ca\u4e86\u903b\u8f91\u548c\u6570\u5b66\u80cc\u540e\u7684\u201cMatrix\u201d\uff1f\u8fd9\u662f\u6709\u53ef\u80fd\u7684\u3002\u4f46\u4e5f\u6709\u53ef\u80fd\u4e3a\u57fa\u7840\u8bed\u8a00\u8003\u8651\u4e00\u79cd\u57fa\u7840\u8bed\u8a00\uff0c\u901a\u8fc7\u5b83\u53ef\u4ee5\u91cd\u5efa\u6240\u6709\u5176\u4ed6\u5185\u5bb9\uff1b\u7136\u800c\uff0c\u8981\u627e\u5230\u8fd9\u79cd\u8bed\u8a00\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u6bd4\u79e9\u5e8f\u548c\u6570\u91cf\u6982\u5ff5\uff08\u7528\u4e8e\u5efa\u7acb\u7b2c\u4e00\u79cd\u57fa\u7840\u8bed\u8a00\u7684\u6982\u5ff5\uff09\u66f4\u4e3a\u57fa\u672c\u7684\u6982\u5ff5\u3002\u5bfb\u627e\u57fa\u7840\u7684\u57fa\u7840\u8bed\u8a00\u610f\u5473\u7740\u8981\u5bf9\u201c\u7406\u89e3\u4e8b\u7269\u201d\u7684\u6700\u57fa\u672c\u65b9\u9762\u8fdb\u884c\u53cd\u601d\u3002\u5982\u679c\u4f60\u6df1\u5165\u4e0b\u53bb\uff0c\u5982\u679c\u4f60\u80fd\u591f\u5230\u8fbe\u5e95\u90e8\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u4f60\u5df2\u7ecf\u770b\u5230\u4e86\u201c\u7406\u89e3\u4e00\u5207\u4e8b\u7269\u7684 Matrix \u80cc\u540e\u7684 Matrix\u201d\uff0c\u800c\u4e14\u8fd9\u79cd\u57fa\u7840\u7684\u53cd\u601d\u8fc7\u7a0b\u53ef\u80fd\u4f1a\u65e0\u9650\u5730\u7ee7\u7eed\u8fdb\u884c\uff0c\u5728\u6bcf\u4e2a\u57fa\u7840\u6b65\u9aa4\u4e2d\u8d4b\u4e88\u77e5\u8bc6\u66f4\u6df1\u4e00\u5c42\u7684\u6df1\u5ea6\u3002<br \/>\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u547d\u9898\u903b\u8f91\u8bed\u8a00 \u6458\u8981 \u672c\u7b14\u8bb0\u5ba1\u67e5\u4e86\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4f5c\u4e3a\u4e00\u79cd\u5143\u8bed\u8a00\uff0c\u7528\u4e8e\u4ece\u7531\u4e24\u4e2a\u7b26\u53f7\u7ec4\u6210\u7684\u57fa\u7840\u8bed\u8a00\u4e2d\u83b7\u5f97\u6709\u6548\u7684\u8868\u8fbe\u5f0f\u3002\u89e3\u91ca\u4e86\u53e5\u6cd5\u89c4\u5219\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u7684\u6982\u5ff5\uff0c\u8fd8\u4ecb\u7ecd\u4e86\u8054\u5408\u5426\u5b9a\u3001\u62ec\u53f7\u548c\u91cd\u6392\u7684\u4f7f\u7528\uff0c\u4ee5\u4fbf\u4e8e\u8868\u8fbe\u5f0f\u7684\u9605\u8bfb\u3002\u6b64\u5916\uff0c\u8fd8\u63d0\u5230\u4e86\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3\u3002\u6700\u540e\uff0c\u5c06\u547d\u9898\u903b\u8f91\u8bed\u8a00\u603b\u7ed3\u4e3a\u6570\u5b66\u548c\u903b\u8f91\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\uff0c\u5e76\u63a2\u8ba8\u4e86\u627e\u5230\u201c\u57fa\u7840\u8bed\u8a00\u7684\u57fa\u7840\u8bed\u8a00\u201d\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u7528\u5b83\u91cd\u5efa\u4e00\u5207\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u90e8\u5206\u540e\uff0c\u671f\u671b\u5b66\u751f\u80fd\u591f\uff1a \u7406\u89e3\u5143\u8bed\u8a00\u7684\u6982\u5ff5\u53ca\u5176\u5728\u547d\u9898\u903b\u8f91\u4e2d\u7684\u5e94\u7528\u3002 \u7406\u89e3\u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u53e5\u6cd5\u89c4\u5219\u3002 \u4e86\u89e3\u547d\u9898\u53d8\u91cf\u7684\u6982\u5ff5\u53ca\u5176\u5728\u6784\u5efa\u8868\u8fbe\u5f0f\u4e2d\u7684\u5e94\u7528\u3002 \u7406\u89e3\u8fde\u63a5\u8bcd\u548c\u8054\u5408\u5426\u5b9a\u5728\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4e2d\u7684\u4f7f\u7528\u3002 \u5b66\u4e60\u4f7f\u7528\u62ec\u53f7\u548c\u91cd\u6392\u4ee5\u4fbf\u4e8e\u9605\u8bfb\u8868\u8fbe\u5f0f\u3002 \u4e86\u89e3\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3\u3002 \u603b\u7ed3\u547d\u9898\u903b\u8f91\u8bed\u8a00\u4f5c\u4e3a\u6570\u5b66\u548c\u903b\u8f91\u4e2d\u7684\u4e00\u9879\u57fa\u672c\u5de5\u5177\u3002 \u601d\u8003\u627e\u5230\u201c\u57fa\u7840\u8bed\u8a00\u7684\u57fa\u7840\u8bed\u8a00\u201d\u7684\u53ef\u80fd\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u7528\u5b83\u91cd\u5efa\u4e00\u5207\u3002 \u5e94\u7528\u6240\u5b66\u6982\u5ff5\u6784\u5efa\u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u3002 \u4f7f\u7528\u547d\u9898\u903b\u8f91\u8bed\u8a00\u6765\u7406\u89e3\u548c\u89e3\u51b3\u6570\u5b66\u548c\u903b\u8f91\u95ee\u9898\u3002 \u76ee\u5f55 \u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u5b57\u6bcd\u8868\u548c\u7b26\u53f7\u4e32 \u4ece\u4e00\u4e2a\u7b26\u53f7\u5f00\u59cb \u7136\u540e\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7 \u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u53e5\u6cd5 \u53e5\u6cd5\u5ba1\u67e5\u793a\u4f8b \u7b26\u53f7\u7ea6\u5b9a \u5143\u53d8\u91cf\u4e0e\u8fde\u63a5\u8bcd \u8054\u5408\u5426\u5b9a\u7684\u4f7f\u7528\u793a\u4f8b \u91cd\u6392\u4e0e\u62ec\u53f7 \u6d3e\u751f\u8fde\u63a5\u8bcd \u547d\u9898\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u53d1\u97f3 \u547d\u9898\u903b\u8f91\u8bed\u8a00\u7684\u603b\u7ed3\u4e0e\u53cd\u601d \u7406\u89e3\u4e00\u5207\u80cc\u540e\u7684\u201c\u77e9\u9635\u201d \u547d\u9898\u903b\u8f91\u8bed\u8a00\uff1a\u5b57\u6bcd\u8868\u548c\u7b26\u53f7\u4e32 \u4ece\u4e00\u4e2a\u7b26\u53f7\u5f00\u59cb \u4e3a\u4e86\u6784\u5efa\u547d\u9898\u903b\u8f91\u8bed\u8a00\uff0c\u6211\u4eec\u5c06\u4ece\u6700\u7b80\u5355\u7684\u5b57\u6bcd\u8868\u5f00\u59cb\uff1a\u4e00\u4e2a\u4ec5\u5305\u542b\u4e00\u4e2a\u7b26\u53f7\u7684\u5b57\u6bcd\u8868\u3002\u7b26\u53f7\u7684\u5f62\u72b6\u5e76\u4e0d\u91cd\u8981\uff0c\u91cd\u8981\u7684\u662f\u5b83\u662f\u552f\u4e00\u7684\u3002\u5982\u679c\u6211\u4eec\u4f7f\u7528\u8fd9\u6837\u7684\u5b57\u6bcd\u8868\u8fdb\u884c\u4e66\u5199\uff0c\u552f\u4e00\u533a\u5206\u7b26\u53f7\u4e32\u7684\u56e0\u7d20\u5c31\u662f\u8be5\u7b26\u53f7\u91cd\u590d\u7684\u6b21\u6570\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u5199\u51fa\u957f\u5ea6\u4e3a \u7684\u7b26\u53f7\u4e32\uff0c\u6211\u4eec\u53ea\u80fd\u5199\u51fa \u4e2a\u4e0d\u540c\u7684\u7b26\u53f7\u4e32\u3002\u6b63\u5982\u4f60\u6240\u89c1\uff0c\u8fd9\u4e2a\u5b57\u6bcd\u8868\u975e\u5e38\u6709\u9650\uff0c\u6ca1\u6709\u592a\u591a\u53ef\u4ee5\u8bf4\u7684\u3002 \u7136\u540e\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7 \u5982\u679c\u6211\u4eec\u4e3a\u5b57\u6bcd\u8868\u6dfb\u52a0\u7b2c\u4e8c\u4e2a\u7b26\u53f7\uff0c\u4e66\u5199\u4f1a\u6bd4\u4e4b\u524d\u7684\u5b57\u6bcd\u8868\u66f4\u4e30\u5bcc\u3002\u73b0\u5728\u6211\u4eec\u53ef\u4ee5\u89c2\u5bdf\u7b26\u53f7\u7684\u6392\u5217\u65b9\u5f0f\uff0c\u4f8b\u5982\uff0c\u5982\u679c \u548c \u662f\u6211\u4eec\u7684\u7b26\u53f7\uff0c\u6211\u4eec\u53ef\u4ee5\u533a\u5206 \u548c \u3002\u4e24\u8005\u90fd\u5305\u542b\u76f8\u540c\u7684\u7b26\u53f7\uff0c\u4f46\u987a\u5e8f\u4e0d\u540c\u3002\u5982\u679c\u6211\u4eec\u80fd\u591f\u5199\u51fa\u6700\u957f\u4e3a \u7684\u7b26\u53f7\u4e32\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5199\u51fa \u4e2a\u957f\u5ea6\u4e3a \u7684\u7b26\u53f7\u4e32\uff0c \u4e2a\u957f\u5ea6\u4e3a \u7684\u7b26\u53f7\u4e32\uff0c \u4e2a\u957f\u5ea6\u4e3a \u7684\u7b26\u53f7\u4e32\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u4e00\u822c\u6765\u8bf4\uff0c \u4e2a\u957f\u5ea6\u4e3a \u7684\u4e0d\u540c\u7b26\u53f7\u4e32\u3002 \u7ec3\u4e60\uff1a\u5728\u7eb8\u4e0a\u5199\u4e0b\u6240\u6709\u53ef\u80fd\u7684\u4e0d\u540c\u7b26\u53f7\u4e32\uff0c\u957f\u5ea6\u4ece \u5230 \u4e0d\u7b49\u3002\u603b\u5171\u53ef\u4ee5\u5199\u51fa\u591a\u5c11\u4e2a\u7b26\u53f7\u4e32\uff1f \u89e3\u7b54\uff1a \u5982\u679c \u662f\u6240\u6709\u7b26\u53f7\u4e32\u7684\u603b\u548c\uff0c\u957f\u5ea6\u4e3a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25133,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[623,575,609],"tags":[],"class_list":["post-25132","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-623","category-575","category-609"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u547d\u9898\u903b\u8f91\u8bed\u8a00 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/zh\/\u547d\u9898\u903b\u8f91\u8bed\u8a00\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u547d\u9898\u903b\u8f91\u8bed\u8a00\" \/>\n<meta property=\"og:description\" content=\"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/zh\/\u547d\u9898\u903b\u8f91\u8bed\u8a00\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-01-18T00:00:25+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-08-28T19:37:24+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-1024x378.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u547d\u9898\u903b\u8f91\u8bed\u8a00\" \/>\n<meta name=\"twitter:description\" content=\"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u547d\u9898\u903b\u8f91\u8bed\u8a00\",\"datePublished\":\"2021-01-18T00:00:25+00:00\",\"dateModified\":\"2024-08-28T19:37:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/\"},\"wordCount\":780,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/11\\\/lenguajedelalogicaproposicional-3.jpg\",\"articleSection\":[\"\u547d\u9898\u903b\u8f91\",\"\u6570\u5b66\",\"\u6570\u7406\u903b\u8f91\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/\",\"name\":\"\u547d\u9898\u903b\u8f91\u8bed\u8a00 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/11\\\/lenguajedelalogicaproposicional-3.jpg\",\"datePublished\":\"2021-01-18T00:00:25+00:00\",\"dateModified\":\"2024-08-28T19:37:24+00:00\",\"description\":\"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/11\\\/lenguajedelalogicaproposicional-3.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/11\\\/lenguajedelalogicaproposicional-3.jpg\",\"width\":1081,\"height\":399,\"caption\":\"toposuranos.com\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u547d\u9898\u903b\u8f91\u8bed\u8a00\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u547d\u9898\u903b\u8f91\u8bed\u8a00 - toposuranos.com\/material","description":"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/zh\/\u547d\u9898\u903b\u8f91\u8bed\u8a00\/","og_locale":"es_ES","og_type":"article","og_title":"\u547d\u9898\u903b\u8f91\u8bed\u8a00","og_description":"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002","og_url":"http:\/\/toposuranos.com\/material\/zh\/\u547d\u9898\u903b\u8f91\u8bed\u8a00\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-01-18T00:00:25+00:00","article_modified_time":"2024-08-28T19:37:24+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-1024x378.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u547d\u9898\u903b\u8f91\u8bed\u8a00","twitter_description":"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u547d\u9898\u903b\u8f91\u8bed\u8a00","datePublished":"2021-01-18T00:00:25+00:00","dateModified":"2024-08-28T19:37:24+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/"},"wordCount":780,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-3.jpg","articleSection":["\u547d\u9898\u903b\u8f91","\u6570\u5b66","\u6570\u7406\u903b\u8f91"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/","url":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/","name":"\u547d\u9898\u903b\u8f91\u8bed\u8a00 - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-3.jpg","datePublished":"2021-01-18T00:00:25+00:00","dateModified":"2024-08-28T19:37:24+00:00","description":"\u5bf9\u547d\u9898\u903b\u8f91\u8bed\u8a00\u8fdb\u884c\u8be6\u7ec6\u63a2\u8ba8\uff0c\u5305\u62ec\u5143\u8bed\u8a00\u6982\u5ff5\u3001\u53e5\u6cd5\u3001\u547d\u9898\u53d8\u91cf\u548c\u8fde\u63a5\u8bcd\u3002","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-3.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/11\/lenguajedelalogicaproposicional-3.jpg","width":1081,"height":399,"caption":"toposuranos.com"},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/zh\/%e5%91%bd%e9%a2%98%e9%80%bb%e8%be%91%e8%af%ad%e8%a8%80\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u547d\u9898\u903b\u8f91\u8bed\u8a00"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/25132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=25132"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/25132\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/25133"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=25132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=25132"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=25132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}