{"id":32334,"date":"2021-05-09T13:00:21","date_gmt":"2021-05-09T13:00:21","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32334"},"modified":"2025-03-03T22:08:31","modified_gmt":"2025-03-03T22:08:31","slug":"%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/","title":{"rendered":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570"},"content":{"rendered":"<style>\n\tp, ul, ol{\n\ttext-align: justify;\n\t}\n\th1{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\t}\n\th2{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\tfont-size:24pt;\n\t}\n\th3 { \n\t\ttext-align: center;\n\t\ttext-transform: uppercase;\n\t\tfont-size: 24px !important;\n\t}\n<\/style>\n<h1>\u5b8c\u6574\u57df\u4e0e\u6574\u6570<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u672c\u8bfe\u7a0b\u4ecb\u7ecd\u4e86\u5b8c\u6574\u57df\u7684\u6982\u5ff5\uff0c\u89e3\u91ca\u4e86\u5176\u5728\u4e00\u822c\u4ee3\u6570\u7814\u7a76\u4e2d\u7684\u91cd\u8981\u6027\uff0c\u5e76\u901a\u8fc7\u6b63\u5f0f\u7684\u6570\u5b66\u8bc1\u660e\u5c55\u793a\u5176\u4e00\u4e9b\u91cd\u8981\u7684\u6027\u8d28\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><em><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><\/em><br \/>\n\u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong> \u4e00\u822c\u4ee3\u6570\u7814\u7a76\u7684\u76ee\u7684\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong> \u5b8c\u6574\u57df\u7684\u6982\u5ff5\u3002<\/li>\n<li><strong>\u89e3\u91ca<\/strong> \u5b8c\u6574\u57df\u4e0e\u6574\u6570\u4e4b\u95f4\u7684\u57fa\u672c\u5171\u540c\u7279\u6027\u3002<\/li>\n<li><strong>\u901a\u8fc7<\/strong> \u6b63\u5f0f\u7684\u6570\u5b66\u8bc1\u660e\uff0c\u5c55\u793a\u5b8c\u6574\u57df\u7684\u57fa\u672c\u6027\u8d28\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<strong><u>\u5185\u5bb9\u76ee\u5f55<\/u><\/strong><br \/>\n<a href=\"#1\">\u4e00\u822c\u4ee3\u6570\u7684\u76ee\u6807\u4e0e\u5148\u5907\u77e5\u8bc6<\/a><br \/>\n<a href=\"#2\">\u4ece\u6574\u6570\u5230\u5b8c\u6574\u57df<\/a><br \/>\n<a href=\"#3\">\u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u57fa\u672c\u5171\u540c\u7279\u6027<\/a><br \/>\n<a href=\"#4\">\u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u6027\u8d28<\/a><br \/>\n<a href=\"#5\">\u7ec3\u4e60<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/hxmc1-eXWxU?si=57GADT52JG4fHFT-\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u4e00\u822c\u4ee3\u6570\u7684\u76ee\u6807\u4e0e\u5148\u5907\u77e5\u8bc6<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=183s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4e00\u822c\u4ee3\u6570\u7684\u4e3b\u8981\u76ee\u6807<\/span><\/strong><\/a> \u662f\u7814\u7a76\u6240\u6709\u53ef\u80fd\u7684\u6570\u5b66\u7cfb\u7edf\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u591a\u4e2a\u8fd9\u6837\u7684\u7cfb\u7edf\uff0c\u5176\u4e2d\u6700\u91cd\u8981\u7684\u5305\u62ec\u81ea\u7136\u6570\u548c\u6574\u6570\uff0c\u5e76\u901a\u8fc7\u540e\u8005\u5f15\u51fa\u5b8c\u6574\u57df\u7684\u6982\u5ff5\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{N}= \\{1,2,3,4,\\cdots\\}<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{Z}= \\{0,\\pm 1,\\pm 2,\\pm 3,\\pm 4,\\cdots\\}<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u4ece\u6574\u6570\u5230\u5b8c\u6574\u57df<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=358s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u5c06\u4ece\u6574\u6570\u5f00\u59cb\u6211\u4eec\u7684\u7814\u7a76\uff0c<\/span><\/strong><\/a> \u4e4b\u6240\u4ee5\u8fd9\u6837\u505a\uff0c\u662f\u56e0\u4e3a\u6574\u6570\u4e0e\u6211\u4eec\u5c06\u5728\u672c\u7814\u7a76\u4e2d\u63a2\u8ba8\u7684\u5927\u591a\u6570\u6570\u7cfb\u5177\u6709\u6700\u591a\u7684\u76f8\u4f3c\u4e4b\u5904\u3002<\/p>\n<p>\u4e0e\u5176\u5c1d\u8bd5\u5b9a\u4e49\u6574\u6570\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u4e0d\u5982\u5047\u8bbe\u65e0\u8bba\u5b83\u4eec\u662f\u4ec0\u4e48\uff0c\u5b83\u4eec\u90fd\u6ee1\u8db3\u67d0\u4e9b\u6027\u8d28\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9009\u62e9\u4e00\u7ec4\u516c\u7406\uff0c\u4f7f\u5f97\u80fd\u591f\u63a8\u5bfc\u51fa\u6240\u6709\u6211\u4eec\u76f4\u89c9\u4e0a\u4e0e\u6574\u6570\u76f8\u5173\u7684\u6027\u8d28\u3002<\/p>\n<p>\u6240\u6709\u8fd9\u4e9b\u90fd\u662f\u901a\u8fc7<strong>\u76ae\u4e9a\u8bfa\u516c\u7406<\/strong>\u6765\u5b9e\u73b0\u7684\uff0c\u5373\u5728\u81ea\u7136\u6570\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\u3002\u901a\u8fc7\u91c7\u7528\u8fd9\u79cd\u516c\u7406\u5316\u65b9\u6cd5\uff0c\u5e76\u6269\u5c55\u81ea\u7136\u6570\u548c\u6574\u6570\u4e0a\u7684\u5404\u79cd\u8fd0\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u65b0\u7684\u6570\u7cfb\uff0c\u4f8b\u5982\u6709\u7406\u6570\u3001\u65e0\u7406\u6570\u3001\u5b9e\u6570\u3001\u590d\u6570\u3001\u56db\u5143\u6570\u3001\u516b\u5143\u6570\u7b49\u7b49\u3002<\/p>\n<p>\u63a5\u7740\uff0c\u5982\u679c\u6211\u4eec\u89c2\u5bdf\u6574\u6570\uff0c\u5c31\u4f1a\u53d1\u73b0\u5b83\u4eec\u5177\u6709\u4e00\u4e9b\u5728\u6240\u6709\u5176\u4ed6\u6570\u7cfb\u4e2d\u90fd\u4f1a\u91cd\u590d\u51fa\u73b0\u7684\u6027\u8d28\uff0c\u4f8b\u5982\u4e58\u6cd5\u5355\u4f4d\u5143\u3001\u52a0\u6cd5\u5355\u4f4d\u5143\u548c\u5206\u914d\u5f8b\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u7814\u7a76\u8fd9\u4e9b\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5efa\u7acb\u4e00\u79cd\u8bed\u8a00\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u540c\u65f6\u8ba8\u8bba\u6240\u6709\u8fd9\u4e9b\u6570\u7cfb\u3002\u5728\u8fd9\u4e00\u80cc\u666f\u4e0b\uff0c\u51fa\u73b0\u4e86\u8bf8\u5982\u4ee5\u4e0b\u7684\u672f\u8bed\uff1a<\/p>\n<ul>\n<li>\u5b8c\u6574\u57df<\/li>\n<li>\u73af<\/li>\n<li>\u7fa4<\/li>\n<li>\u5411\u91cf\u7a7a\u95f4<\/li>\n<\/ul>\n<p>\u4ee5\u53ca\u8bb8\u591a\u7c7b\u4f3c\u7684\u6570\u5b66\u6982\u5ff5\u3002\u6211\u4eec\u5c06\u9996\u5148\u96c6\u4e2d\u7cbe\u529b\u7814\u7a76<strong>\u5b8c\u6574\u57df\u3002<\/strong><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u57fa\u672c\u5171\u540c\u7279\u6027<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=472s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4e3a\u4e86\u8bf4\u660e\u4ec0\u4e48\u662f\u5b8c\u6574\u57df<\/span><\/strong><\/a>\uff0c\u6211\u4eec\u5c06\u5229\u7528\u6211\u4eec\u5bf9\u6574\u6570\u7684\u6df1\u5165\u7406\u89e3\u3002\u5728\u6b64\u80cc\u666f\u4e0b\uff0c\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u662f\u6574\u6570\uff0c\u5219\u6ee1\u8db3\u4ee5\u4e0b<strong>\u5b9a\u5f8b<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u4ea4\u6362\u5f8b\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = b + a<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab = ba<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u7ed3\u5408\u5f8b\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a+b+c = (a+b)+c<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(ab)c = abc = a(bc)<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u5206\u914d\u5f8b\uff1a<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a(b+c) = ab+ac<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>\u9664\u6b64\u4e4b\u5916\uff0c\u8fd8\u5b58\u5728\u67d0\u4e9b\u7279\u6b8a\u5143\u7d20\uff0c\u88ab\u79f0\u4e3a\u5355\u4f4d\u5143\u3002<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u5355\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = a \\leftrightarrow c=0<\/span><\/span><\/li>\n<li><strong>\u4e58\u6cd5\u5355\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ac = a \\leftrightarrow c=1<\/span><\/span><\/li>\n<\/ul>\n<p>\u7b26\u53f7 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u8868\u793a\u52a0\u6cd5\u5355\u4f4d\u5143\uff0c\u800c\u7b26\u53f7 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u8868\u793a\u4e58\u6cd5\u5355\u4f4d\u5143\u3002<\/p>\n<p>\u6574\u6570\u8fd8\u5177\u6709\u52a0\u6cd5\u9006\u5143\u3002\u6bcf\u4e2a\u6574\u6570\u90fd\u6709\u4e00\u4e2a\u52a0\u6cd5\u9006\u5143\uff0c\u4e0e\u5176\u76f8\u52a0\u540e\u5f97\u5230\u52a0\u6cd5\u5355\u4f4d\u5143\u3002<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u9006\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = 0 \\longleftrightarrow c=-a<\/span><\/span><\/li>\n<\/ul>\n<p>\u52a0\u6cd5\u9006\u5143\u901a\u5e38\u4ee5\u7b26\u53f7 \u00ab-\u00bb \u8868\u793a\u3002<\/p>\n<p>\u6700\u540e\uff0c\u8fd8\u5b58\u5728\u4e00\u4e2a<strong>\u6d88\u53bb\u5f8b<\/strong>\uff0c\u5176\u6570\u5b66\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(c\\neq 0 \\wedge ca = cb) \\longleftrightarrow (a=b)<\/span><\/span><\/p>\n<p>\u8fd9\u4e9b\u6211\u4eec\u8ba8\u8bba\u7684\u6027\u8d28\u9002\u7528\u4e8e\u8bb8\u591a\u5176\u4ed6\u96c6\u5408\uff0c\u4f8b\u5982\u5b9e\u6570\u3001\u590d\u6570\u3001\u591a\u9879\u5f0f\u7b49\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u79f0<strong>\u5b8c\u6574\u57df<\/strong>\u4e3a\u6240\u6709\u6ee1\u8db3\u8fd9\u4e9b\u6027\u8d28\u7684\u96c6\u5408\u3002<\/p>\n<p><span style=\"color: #800000;\"><strong>\u5b9a\u4e49\uff1a<\/strong><\/span> \u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u662f\u4e00\u4e2a\u96c6\u5408\uff0c\u5e76\u4e14\u5728\u5176\u4e0a\u5b9a\u4e49\u4e86\u52a0\u6cd5\u548c\u4e58\u6cd5\u8fd0\u7b97\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u5b8c\u6574\u57df\u5f53\u4e14\u4ec5\u5f53\uff1a<\/p>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow a+b \\in D<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow ab \\in D<\/span><\/span><\/li>\n<\/ul>\n<p>\u6b64\u5916\uff0c\u8fd8\u9700\u6ee1\u8db3<strong>\u7ed3\u5408\u5f8b\u3001\u4ea4\u6362\u5f8b<\/strong>\u548c<strong>\u5206\u914d\u5f8b<\/strong>\uff0c\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u9700\u8981\u5305\u542b<strong>\u52a0\u6cd5\u5355\u4f4d\u5143<\/strong>\u548c<strong>\u4e58\u6cd5\u5355\u4f4d\u5143<\/strong>\uff08\u5b83\u4eec\u662f\u552f\u4e00\u7684\uff09\uff0c\u5e76\u4e14\u8fd8\u5fc5\u987b\u6ee1\u8db3<strong>\u6d88\u53bb\u5f8b<\/strong>\u3002<\/p>\n<h4>\u5b8c\u6574\u57df\u7684\u793a\u4f8b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=749s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8003\u8651\u96c6\u5408 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\{a+b\\sqrt{3}\\; |\\; a,b\\in \\mathbb{Z}\\}.<\/span><\/span><\/span> <\/strong><\/a>\u8be5\u96c6\u5408\u5728\u901a\u5e38\u7684\u52a0\u6cd5\u4e0e\u4e58\u6cd5\u8fd0\u7b97\u4e0b\u6784\u6210\u4e00\u4e2a\u5b8c\u6574\u57df\uff0c\u56e0\u4e3a\u5b83\u6ee1\u8db3\u4ea4\u6362\u5f8b\u3001\u7ed3\u5408\u5f8b\u548c\u5206\u914d\u5f8b\uff0c\u5e76\u4e14\u5177\u6709\u52a0\u6cd5\u5355\u4f4d\u5143\u3001\u4e58\u6cd5\u5355\u4f4d\u5143\u4ee5\u53ca\u52a0\u6cd5\u9006\u5143\u3002<\/p>\n<ul>\n<li><strong>\u52a0\u6cd5\u5355\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u4e58\u6cd5\u5355\u4f4d\u5143\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u52a0\u6cd5\u9006\u5143\uff1a<\/strong> \u6bcf\u4e2a\u5143\u7d20 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b\\sqrt{3}<\/span><\/span> \u90fd\u6709\u52a0\u6cd5\u9006\u5143 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-a-b\\sqrt{3}<\/span><\/span><\/li>\n<\/ul>\n<p>\u6700\u91cd\u8981\u7684\u662f\uff0c\u8be5\u96c6\u5408 A \u5bf9\u52a0\u6cd5\u548c\u4e58\u6cd5\u5c01\u95ed\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in A<\/span><\/span>\uff0c\u5219 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x+y\\in A<\/span><\/span> \u4e14 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xy\\in A.<\/span><\/span> \u8fd9\u4e00\u70b9\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u9a8c\u8bc1\uff1a\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_1 + b_1\\sqrt{3}<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_2 + b_2\\sqrt{3}<\/span><\/span> \u662f <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u7684\u5143\u7d20\uff0c\u5219<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n(a_1 + b_1\\sqrt{3}) + (a_2 + b_2\\sqrt{3}) &amp;=(a_1+a_2) + (b_1 + b_2)\\sqrt{3} \\in A\\\\ \\\\\n\n(a_1 + b_1\\sqrt{3})  (a_2 + b_2\\sqrt{3})  &amp;= a_1a_2 + a_1b_2\\sqrt{3}+b_1a_2\\sqrt{3} + 3b_1b_2 \\\\\n\n&amp;=(a_1a_2 + 3b_1b_2) + (a_1b_2 + b_1a_2)\\sqrt{3} \\in A\n\n\\end{array}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/y6jXNPhjKv4?si=9SaXhWHN42sC73lZ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u6027\u8d28<\/h3>\n<h4>\u5b8c\u6574\u57df\u7684\u52a0\u6cd5\u5355\u4f4d\u5143\u662f\u552f\u4e00\u7684<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=26s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u4e00\u70b9\u53ef\u4ee5\u901a\u8fc7\u53cd\u8bc1\u6cd5\u8bc1\u660e\uff1a<\/span><\/strong><\/a> \u5047\u8bbe\u5b58\u5728\u4e24\u4e2a\u52a0\u6cd5\u5355\u4f4d\u5143\uff0c\u5206\u522b\u8bb0\u4f5c <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0^\\prime<\/span><\/span>\uff0c\u90a3\u4e48\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; 0\\neq 0^\\prime &amp; \\text{; \u5047\u8bbe}\\\\\n\n(2) &amp; a+0 = a &amp; \\text{; \u5047\u8bbe\uff1a$0$ \u662f\u52a0\u6cd5\u5355\u4f4d\u5143}\\\\\n\n(3) &amp; b+0^\\prime = b &amp; \\text{; \u5047\u8bbe\uff1a$0^\\prime$ \u662f\u52a0\u6cd5\u5355\u4f4d\u5143}\\\\\n\n(4) &amp; 0^\\prime + 0 = 0^\\prime &amp; \\text{; \u5728 $(2)$ \u4e2d\u4ee4 $a=0^\\prime$}\\\\\n\n(5) &amp; 0 + 0^\\prime = 0 &amp; \\text{; \u5728 $(3)$ \u4e2d\u4ee4 $b=0$}\\\\\n\n(6) &amp; 0 = 0^\\prime  &amp; \\text{; \u7531 $(4,5)$ \u53ca\u52a0\u6cd5\u4ea4\u6362\u5f8b}\\\\\n\n(7) &amp; \\bot &amp;\\text{; \u7531 $(1,6)$ \u5f97\u77db\u76fe}\n\n\\end{array}<\/span>\n<p>\u7531\u6b64\u63a8\u7406\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0 \\neq 0^\\prime, a + 0 = a, b + 0^\\prime = b\\}\\vdash \\bot.<\/span><\/span><\/p>\n<p>\u56e0\u6b64\uff0c\u901a\u8fc7\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u8bc1\u660e\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{a + 0 = a, b + 0^\\prime = b\\}\\vdash 0 = 0^\\prime.<\/span><\/span><\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u5b58\u5728\u4e24\u4e2a\u52a0\u6cd5\u5355\u4f4d\u5143\uff0c\u5b83\u4eec\u5fc5\u7136\u662f\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u52a0\u6cd5\u5355\u4f4d\u5143\u662f\u552f\u4e00\u7684\u3002<\/p>\n<h4>\u4e58\u6cd5\u5355\u4f4d\u5143\u4e5f\u662f\u552f\u4e00\u7684<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=305s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8bc1\u660e\u65b9\u6cd5\u4e0e\u4e0a\u9762\u7684\u52a0\u6cd5\u5355\u4f4d\u5143\u552f\u4e00\u6027\u8bc1\u660e\u7c7b\u4f3c\u3002<\/span><\/strong><\/a> \u5047\u8bbe\u5b58\u5728\u4e24\u4e2a\u4e58\u6cd5\u5355\u4f4d\u5143 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^\\prime<\/span><\/span>\uff0c\u5219\u53ef\u4ee5\u8fdb\u884c\u5982\u4e0b\u63a8\u7406\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; 1\\neq 1^\\prime &amp; \\text{; \u5047\u8bbe}\\\\\n\n(2) &amp; 1\\cdot a = a &amp; \\text{; \u5047\u8bbe\uff1a$1$ \u662f\u4e58\u6cd5\u5355\u4f4d\u5143}\\\\\n\n(3) &amp; 1^\\prime \\cdot b = b &amp; \\text{; \u5047\u8bbe\uff1a$1^\\prime$ \u662f\u4e58\u6cd5\u5355\u4f4d\u5143}\\\\\n\n(4) &amp; 1\\cdot 1^\\prime = 1^\\prime &amp; \\text{; \u5728 $(2)$ \u4e2d\u4ee4 $a=1^\\prime$}\\\\\n\n(5) &amp; 1^\\prime \\cdot 1 = 1 &amp; \\text{; \u5728 $(3)$ \u4e2d\u4ee4 $b=1$}\\\\\n\n(6) &amp; 1 = 1^\\prime  &amp; \\text{; \u7531 $(4,5)$ \u53ca\u4e58\u6cd5\u4ea4\u6362\u5f8b}\\\\\n\n(7) &amp; \\bot &amp;\\text{; \u7531 $(1,6)$ \u5f97\u77db\u76fe}\n\n\\end{array}<\/span>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{1 \\neq 1^\\prime, 1a= a, 1b = b\\}\\vdash \\bot.<\/span><\/span><\/p>\n<p>\u7531\u6b64\uff0c\u901a\u8fc7\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u63a8\u51fa\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{1a= a, 1b= b\\}\\vdash 1 = 1^\\prime.<\/span><\/span><\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u5b58\u5728\u4e24\u4e2a\u4e58\u6cd5\u5355\u4f4d\u5143\uff0c\u5b83\u4eec\u5fc5\u7136\u662f\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u4e58\u6cd5\u5355\u4f4d\u5143\u662f\u552f\u4e00\u7684\u3002<\/p>\n<h4>\u52a0\u6cd5\u6ee1\u8db3\u6d88\u53bb\u5f8b<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=461s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u5c31\u662f\u6211\u4eec\u5728\u7b49\u5f0f\u4e2d<\/span><\/strong><\/a> \u6d88\u53bb\u76f8\u540c\u9879\u7684\u4f9d\u636e\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = a+c \\longleftrightarrow b = c<\/span><\/span><\/p>\n<p>\u8bc1\u660e\u8fd9\u4e00\u70b9\u5e76\u4e0d\u96be\uff0c\u53ea\u9700\u8fdb\u884c\u4ee5\u4e0b\u63a8\u7406\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a+b = a+c &amp; \\text{; \u5047\u8bbe} \\\\\n\n(2) &amp; a+b-a = a+c-a &amp; \\text{; \u7531$(1)$\uff0c\u5bf9\u7b49\u5f0f\u4e24\u8fb9\u52a0 $-a$} \\\\\n\n(3) &amp; (a-a)+b = (a-a)+c &amp; \\text{; \u7531$(2)$\uff0c\u7ed3\u5408\u4ea4\u6362\u5f8b\u548c\u7ed3\u5408\u5f8b} \\\\\n\n(4) &amp; 0+b = 0+c &amp; \\text{; \u7531$(3)$\uff0c\u52a0\u6cd5\u9006\u5143\u7684\u5b9a\u4e49} \\\\\n\n(5) &amp; b = c &amp; \\text{; \u7531$(4)$\uff0c\u52a0\u6cd5\u5355\u4f4d\u5143\u7684\u6027\u8d28} \\\\\n\n\\end{array}<\/span>\n<p>\u7531\u4e8e\u8be5\u63a8\u7406\u53ef\u4ee5\u9006\u5411\u8fdb\u884c\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b=a+c \\dashv \\vdash b=c<\/span><\/span><\/p>\n<p>\u8fd9\u7b49\u4ef7\u4e8e\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash a+b=a+c \\longleftrightarrow b=c<\/span><\/span><\/p>\n<h4>\u52a0\u6cd5\u5355\u4f4d\u5143\u540c\u65f6\u4e5f\u662f\u4e58\u6cd5\u7684\u5438\u6536\u5143<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=632s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u4e00\u6027\u8d28\u610f\u5473\u7740<\/span><\/strong><\/a>\uff0c\u5bf9\u4e8e\u6240\u6709\u5b8c\u6574\u57df\u4e2d\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\uff0c\u6709\uff1a<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 0 = 0<\/span><\/span><\/p>\n<p>\u8bc1\u660e\u8fd9\u4e2a\u7ed3\u8bba\u4e5f\u5f88\u7b80\u5355\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u63a8\u7406\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+0) &amp; \\text{; \u7531\u5206\u914d\u5f8b} \\\\\n\n(2) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+a-a) &amp; \\text{; \u7531$(1)$\uff0c\u52a0\u6cd5\u9006\u5143\u7684\u5b9a\u4e49} \\\\\n\n(3) &amp; a\\cdot a + a\\cdot 0 = a\\cdot a + a\\cdot a - a\\cdot a &amp; \\text{; \u7531$(2)$\uff0c\u518d\u6b21\u5e94\u7528\u5206\u914d\u5f8b} \\\\\n\n(4) &amp; a\\cdot 0 =  a\\cdot a - a\\cdot a &amp; \\text{; \u7531$(3)$\uff0c\u52a0\u6cd5\u6d88\u53bb\u5f8b} \\\\\n\n(5) &amp; a\\cdot 0 =  0 &amp; \\text{; \u7531$(4)$\uff0c\u52a0\u6cd5\u9006\u5143\u7684\u5b9a\u4e49} \\\\\n\n\\end{array}<\/span>\n<h4><strong>\u7b26\u53f7\u6cd5\u5219\uff1a<\/strong><\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=736s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u76f8\u540c\u7b26\u53f7\u7684\u4e24\u4e2a\u6570\u76f8\u4e58<\/span><\/strong><\/a> \u7ed3\u679c\u59cb\u7ec8\u4e3a\u6b63\uff1b\u4e0d\u540c\u7b26\u53f7\u7684\u4e24\u4e2a\u6570\u76f8\u4e58\u7ed3\u679c\u59cb\u7ec8\u4e3a\u8d1f\u3002\u8fd9\u4e00\u6027\u8d28\u7684\u8bc1\u660e\u4e5f\u5f88\u7b80\u5355\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot b = a\\cdot b + 0 &amp; \\text{; \u52a0\u6cd5\u5355\u4f4d\u5143} \\\\\n\n(2) &amp; a\\cdot b = a\\cdot b + (a)\\cdot(-b) - (a)\\cdot(-b) &amp; \\text{; \u7531$(1)$ \u548c\u52a0\u6cd5\u9006\u5143} \\\\\n\n(3) &amp; a\\cdot b = a\\cdot (b -b) - (a)\\cdot(-b) &amp; \\text{; \u7531$(2)$ \u548c\u52a0\u6cd5\u9006\u5143} \\\\\n\n(4) &amp; a\\cdot b = a\\cdot 0 + (-a)\\cdot(-b) &amp; \\text{; \u7531$(3)$ \u548c\u52a0\u6cd5\u9006\u5143} \\\\\n\n(5) &amp; a\\cdot b = (-a)\\cdot(-b) &amp; \\text{; \u7531$(4)$ \u548c\u4e58\u6cd5\u5438\u6536\u5143} \\\\\n\n\\end{array}<\/span>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u5230\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> ab = (-a)(-b)<\/span><\/span><\/p>\n<p>\u5bf9\u4e8e\u4e0d\u540c\u7b26\u53f7\u7684\u60c5\u51b5\uff0c\u63a8\u5bfc\u65b9\u5f0f\u7c7b\u4f3c\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; a\\cdot(-b) = a \\cdot (-b) + 0 &amp; \\text{; \u52a0\u6cd5\u5355\u4f4d\u5143} \\\\\n\n(2) &amp; a\\cdot(-b) = a \\cdot (-b) + a \\cdot b  -  a \\cdot b  &amp; \\text{; \u7531$(1)$ \u548c\u52a0\u6cd5\u9006\u5143} \\\\\n\n(3) &amp; a\\cdot(-b) = a \\cdot (b-b)  -  a \\cdot b  &amp; \\text{; \u7531$(2)$ \u548c\u5206\u914d\u5f8b} \\\\\n\n(4) &amp; a\\cdot(-b) = a \\cdot 0  -  a \\cdot b  &amp; \\text{; \u7531$(3)$ \u548c\u52a0\u6cd5\u9006\u5143} \\\\\n\n(5) &amp; a\\cdot(-b) = - a \\cdot b  &amp; \\text{; \u7531$(4)$ \u548c\u4e58\u6cd5\u5438\u6536\u5143} \\\\\n\n\\end{array}<\/span>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u5230\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b) = -a(b)<\/span><\/span><\/p>\n<h4>\u5982\u679c\u4e24\u4e2a\u6570\u7684\u4e58\u79ef\u4e3a\u96f6\uff0c\u5219\u81f3\u5c11\u6709\u4e00\u4e2a\u6570\u4e3a\u96f6<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=875s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u53e6\u4e00\u4e2a\u5e38\u7528\u7684\u91cd\u8981\u6027\u8d28<\/span><\/strong><\/a> \u662f\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab=0 \\leftrightarrow (a=0 \\vee b=0)<\/span><\/span><\/p>\n<p>\u5176\u8bc1\u660e\u4e5f\u5f88\u76f4\u63a5\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\{a=0\\} \\models a\\cdot b = 0  &amp; \\textbf{; \u4e58\u6cd5\u5438\u6536\u5143} \\\\\n\n(2) &amp; \\models a=0 \\rightarrow a\\cdot b = 0  &amp;\\text{; \u7531$(1)$} \\\\\n\n(3) &amp; \\models \\neg (a\\cdot b = 0 ) \\rightarrow \\neg(a=0) &amp;\\text{; \u9006\u5426\u547d\u9898$(2)$} \\\\\n\n(4) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(a=0) &amp;\\text{; \u7531$(3)$} \\\\\n\n(5) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(b=0) &amp;\\text{; \u540c\u7406$(4)$} \\\\\n\n(6) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models  \\neg(a=0) \\wedge \\neg(b=0) &amp;\\text{; \u5408\u53d6\u5f15\u5165$(4,5)$} \\\\\n\n(7) &amp; \\models (\\neg (a\\cdot b = 0 )) \\rightarrow \\neg(a=0) \\wedge \\neg(b=0)  &amp;\\text{; \u7531$(6)$} \\\\\n\n(8) &amp; \\models \\neg(\\neg(a=0) \\wedge \\neg(b=0) ) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{; \u9006\u5426\u547d\u9898$(7)$} \\\\\n\n(9) &amp; \\models (a=0 \\vee b=0) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{; \u7531\u5fb7\u6469\u6839\u5b9a\u5f8b$(8)$} \\\\\n\n(10)&amp; \\{a\\neq 0 , a\\cdot b=0\\} \\models b=0 &amp; \\textbf{; \u4e58\u6cd5\u5438\u6536\u5143} \\\\\n\n(11)&amp; \\{a\\cdot b=0\\} \\models a\\neq 0 \\rightarrow  b=0 &amp; \\text{; \u7531$(10)$} \\\\\n\n(12)&amp; \\{a\\cdot b=0\\} \\models \\neg(a\\neq 0) \\vee  b=0 &amp; \\text{; \u8574\u542b\u5b9a\u4e49$(11)$} \\\\\n\n(13)&amp; \\{a\\cdot b=0\\} \\models a=0 \\vee  b=0 &amp; \\text{; \u53cc\u91cd\u5426\u5b9a$(12)$} \\\\\n\n(14)&amp; \\models (a\\cdot b=0) \\rightarrow (a=0 \\vee  b=0) &amp; \\text{; \u7531$(13)$} \\\\\n\n(15)&amp; \\models (a\\cdot b=0) \\leftrightarrow (a=0 \\vee  b=0) &amp; \\text{; \u7531$(9,14)$} \\\\\n\n\\end{array}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KZQ3PXeMlKk?si=O_Hek5KFG853Q6qT\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u7ec3\u4e60<\/h2>\n<p>\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u662f\u5b8c\u6574\u57df <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u4e2d\u7684\u4efb\u610f\u5143\u7d20\u3002\u8bc1\u660e\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(-a)=(-1)a<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=306s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(a+b)=(-a) + (-b)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=827s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b)=-(ab)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1213s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(-a)=a<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1628s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(b-c) = ab - ac<\/span><\/span> <strong>[\u5f85\u8bc1\u660e]<\/strong><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)+(b-c) = a-c<\/span><\/span> <strong>[\u5f85\u8bc1\u660e]<\/strong><\/li>\n<li>\u5bf9\u4e8e\u6240\u6709 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in D<\/span><\/span>\uff0c\u5b58\u5728\u552f\u4e00\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u4f7f\u5f97 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 1 = a<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=2029s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u7b54]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xx = x \\leftrightarrow (x=1 \\vee x=0)<\/span><\/span> <strong>[\u5f85\u8bc1\u660e]<\/strong><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u5b8c\u6574\u57df\u4e0e\u6574\u6570 \u6458\u8981\uff1a \u672c\u8bfe\u7a0b\u4ecb\u7ecd\u4e86\u5b8c\u6574\u57df\u7684\u6982\u5ff5\uff0c\u89e3\u91ca\u4e86\u5176\u5728\u4e00\u822c\u4ee3\u6570\u7814\u7a76\u4e2d\u7684\u91cd\u8981\u6027\uff0c\u5e76\u901a\u8fc7\u6b63\u5f0f\u7684\u6570\u5b66\u8bc1\u660e\u5c55\u793a\u5176\u4e00\u4e9b\u91cd\u8981\u7684\u6027\u8d28\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u7406\u89e3 \u4e00\u822c\u4ee3\u6570\u7814\u7a76\u7684\u76ee\u7684\u3002 \u7406\u89e3 \u5b8c\u6574\u57df\u7684\u6982\u5ff5\u3002 \u89e3\u91ca \u5b8c\u6574\u57df\u4e0e\u6574\u6570\u4e4b\u95f4\u7684\u57fa\u672c\u5171\u540c\u7279\u6027\u3002 \u901a\u8fc7 \u6b63\u5f0f\u7684\u6570\u5b66\u8bc1\u660e\uff0c\u5c55\u793a\u5b8c\u6574\u57df\u7684\u57fa\u672c\u6027\u8d28\u3002 \u5185\u5bb9\u76ee\u5f55 \u4e00\u822c\u4ee3\u6570\u7684\u76ee\u6807\u4e0e\u5148\u5907\u77e5\u8bc6 \u4ece\u6574\u6570\u5230\u5b8c\u6574\u57df \u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u57fa\u672c\u5171\u540c\u7279\u6027 \u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u6027\u8d28 \u7ec3\u4e60 \u4e00\u822c\u4ee3\u6570\u7684\u76ee\u6807\u4e0e\u5148\u5907\u77e5\u8bc6 \u4e00\u822c\u4ee3\u6570\u7684\u4e3b\u8981\u76ee\u6807 \u662f\u7814\u7a76\u6240\u6709\u53ef\u80fd\u7684\u6570\u5b66\u7cfb\u7edf\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u591a\u4e2a\u8fd9\u6837\u7684\u7cfb\u7edf\uff0c\u5176\u4e2d\u6700\u91cd\u8981\u7684\u5305\u62ec\u81ea\u7136\u6570\u548c\u6574\u6570\uff0c\u5e76\u901a\u8fc7\u540e\u8005\u5f15\u51fa\u5b8c\u6574\u57df\u7684\u6982\u5ff5\u3002 \u4ece\u6574\u6570\u5230\u5b8c\u6574\u57df \u6211\u4eec\u5c06\u4ece\u6574\u6570\u5f00\u59cb\u6211\u4eec\u7684\u7814\u7a76\uff0c \u4e4b\u6240\u4ee5\u8fd9\u6837\u505a\uff0c\u662f\u56e0\u4e3a\u6574\u6570\u4e0e\u6211\u4eec\u5c06\u5728\u672c\u7814\u7a76\u4e2d\u63a2\u8ba8\u7684\u5927\u591a\u6570\u6570\u7cfb\u5177\u6709\u6700\u591a\u7684\u76f8\u4f3c\u4e4b\u5904\u3002 \u4e0e\u5176\u5c1d\u8bd5\u5b9a\u4e49\u6574\u6570\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u4e0d\u5982\u5047\u8bbe\u65e0\u8bba\u5b83\u4eec\u662f\u4ec0\u4e48\uff0c\u5b83\u4eec\u90fd\u6ee1\u8db3\u67d0\u4e9b\u6027\u8d28\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9009\u62e9\u4e00\u7ec4\u516c\u7406\uff0c\u4f7f\u5f97\u80fd\u591f\u63a8\u5bfc\u51fa\u6240\u6709\u6211\u4eec\u76f4\u89c9\u4e0a\u4e0e\u6574\u6570\u76f8\u5173\u7684\u6027\u8d28\u3002 \u6240\u6709\u8fd9\u4e9b\u90fd\u662f\u901a\u8fc7\u76ae\u4e9a\u8bfa\u516c\u7406\u6765\u5b9e\u73b0\u7684\uff0c\u5373\u5728\u81ea\u7136\u6570\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u57fa\u672c\u7684\u7b97\u672f\u8fd0\u7b97\u3002\u901a\u8fc7\u91c7\u7528\u8fd9\u79cd\u516c\u7406\u5316\u65b9\u6cd5\uff0c\u5e76\u6269\u5c55\u81ea\u7136\u6570\u548c\u6574\u6570\u4e0a\u7684\u5404\u79cd\u8fd0\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u65b0\u7684\u6570\u7cfb\uff0c\u4f8b\u5982\u6709\u7406\u6570\u3001\u65e0\u7406\u6570\u3001\u5b9e\u6570\u3001\u590d\u6570\u3001\u56db\u5143\u6570\u3001\u516b\u5143\u6570\u7b49\u7b49\u3002 \u63a5\u7740\uff0c\u5982\u679c\u6211\u4eec\u89c2\u5bdf\u6574\u6570\uff0c\u5c31\u4f1a\u53d1\u73b0\u5b83\u4eec\u5177\u6709\u4e00\u4e9b\u5728\u6240\u6709\u5176\u4ed6\u6570\u7cfb\u4e2d\u90fd\u4f1a\u91cd\u590d\u51fa\u73b0\u7684\u6027\u8d28\uff0c\u4f8b\u5982\u4e58\u6cd5\u5355\u4f4d\u5143\u3001\u52a0\u6cd5\u5355\u4f4d\u5143\u548c\u5206\u914d\u5f8b\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u7814\u7a76\u8fd9\u4e9b\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5efa\u7acb\u4e00\u79cd\u8bed\u8a00\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u540c\u65f6\u8ba8\u8bba\u6240\u6709\u8fd9\u4e9b\u6570\u7cfb\u3002\u5728\u8fd9\u4e00\u80cc\u666f\u4e0b\uff0c\u51fa\u73b0\u4e86\u8bf8\u5982\u4ee5\u4e0b\u7684\u672f\u8bed\uff1a \u5b8c\u6574\u57df \u73af \u7fa4 \u5411\u91cf\u7a7a\u95f4 \u4ee5\u53ca\u8bb8\u591a\u7c7b\u4f3c\u7684\u6570\u5b66\u6982\u5ff5\u3002\u6211\u4eec\u5c06\u9996\u5148\u96c6\u4e2d\u7cbe\u529b\u7814\u7a76\u5b8c\u6574\u57df\u3002 \u5b8c\u6574\u57df\u4e0e\u6574\u6570\u7684\u57fa\u672c\u5171\u540c\u7279\u6027 \u4e3a\u4e86\u8bf4\u660e\u4ec0\u4e48\u662f\u5b8c\u6574\u57df\uff0c\u6211\u4eec\u5c06\u5229\u7528\u6211\u4eec\u5bf9\u6574\u6570\u7684\u6df1\u5165\u7406\u89e3\u3002\u5728\u6b64\u80cc\u666f\u4e0b\uff0c\u5982\u679c \u3001 \u548c \u662f\u6574\u6570\uff0c\u5219\u6ee1\u8db3\u4ee5\u4e0b\u5b9a\u5f8b\uff1a \u4ea4\u6362\u5f8b\uff1a \u7ed3\u5408\u5f8b\uff1a \u5206\u914d\u5f8b\uff1a \u9664\u6b64\u4e4b\u5916\uff0c\u8fd8\u5b58\u5728\u67d0\u4e9b\u7279\u6b8a\u5143\u7d20\uff0c\u88ab\u79f0\u4e3a\u5355\u4f4d\u5143\u3002 \u52a0\u6cd5\u5355\u4f4d\u5143\uff1a \u4e58\u6cd5\u5355\u4f4d\u5143\uff1a \u7b26\u53f7 \u8868\u793a\u52a0\u6cd5\u5355\u4f4d\u5143\uff0c\u800c\u7b26\u53f7 \u8868\u793a\u4e58\u6cd5\u5355\u4f4d\u5143\u3002 \u6574\u6570\u8fd8\u5177\u6709\u52a0\u6cd5\u9006\u5143\u3002\u6bcf\u4e2a\u6574\u6570\u90fd\u6709\u4e00\u4e2a\u52a0\u6cd5\u9006\u5143\uff0c\u4e0e\u5176\u76f8\u52a0\u540e\u5f97\u5230\u52a0\u6cd5\u5355\u4f4d\u5143\u3002 \u52a0\u6cd5\u9006\u5143\uff1a \u52a0\u6cd5\u9006\u5143\u901a\u5e38\u4ee5\u7b26\u53f7 \u00ab-\u00bb \u8868\u793a\u3002 \u6700\u540e\uff0c\u8fd8\u5b58\u5728\u4e00\u4e2a\u6d88\u53bb\u5f8b\uff0c\u5176\u6570\u5b66\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a \u8fd9\u4e9b\u6211\u4eec\u8ba8\u8bba\u7684\u6027\u8d28\u9002\u7528\u4e8e\u8bb8\u591a\u5176\u4ed6\u96c6\u5408\uff0c\u4f8b\u5982\u5b9e\u6570\u3001\u590d\u6570\u3001\u591a\u9879\u5f0f\u7b49\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u79f0\u5b8c\u6574\u57df\u4e3a\u6240\u6709\u6ee1\u8db3\u8fd9\u4e9b\u6027\u8d28\u7684\u96c6\u5408\u3002 \u5b9a\u4e49\uff1a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32317,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1035,575],"tags":[],"class_list":["post-32334","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1035","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u5b8c\u6574\u57df\u4e0e\u6574\u6570 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/zh\/\u5b8c\u6574\u57df\u4e0e\u6574\u6570\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5b8c\u6574\u57df\u4e0e\u6574\u6570\" \/>\n<meta property=\"og:description\" content=\"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/zh\/\u5b8c\u6574\u57df\u4e0e\u6574\u6570\/\" \/>\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=\"2021-05-09T13:00:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-03-03T22:08:31+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u5b8c\u6574\u57df\u4e0e\u6574\u6570\" \/>\n<meta name=\"twitter:description\" content=\"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u5b8c\u6574\u57df\u4e0e\u6574\u6570\",\"datePublished\":\"2021-05-09T13:00:21+00:00\",\"dateModified\":\"2025-03-03T22:08:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/\"},\"wordCount\":799,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/algebrageneral.jpg\",\"articleSection\":[\"\u4e00\u822c\u4ee3\u6570\",\"\u6570\u5b66\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/\",\"name\":\"\u5b8c\u6574\u57df\u4e0e\u6574\u6570 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/algebrageneral.jpg\",\"datePublished\":\"2021-05-09T13:00:21+00:00\",\"dateModified\":\"2025-03-03T22:08:31+00:00\",\"description\":\"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/algebrageneral.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/algebrageneral.jpg\",\"width\":1792,\"height\":1024,\"caption\":\"Dominios de Integridad, Integrity Domains, Dom\u00ednios de Integridade, \u6574\u6570\u57df, \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629, \u0905\u0916\u0902\u0921\u0924\u093e \u0921\u094b\u092e\u0947\u0928, \u0414\u043e\u043c\u0435\u043d\u044b \u0446\u0435\u043b\u043e\u0441\u0442\u043d\u043e\u0441\u0442\u0438, Domaines d'Int\u00e9grit\u00e9\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u5b8c\u6574\u57df\u4e0e\u6574\u6570\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/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\":\"https:\\\/\\\/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\":\"https:\\\/\\\/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\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570 - toposuranos.com\/material","description":"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\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":"https:\/\/toposuranos.com\/material\/zh\/\u5b8c\u6574\u57df\u4e0e\u6574\u6570\/","og_locale":"es_ES","og_type":"article","og_title":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570","og_description":"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002","og_url":"https:\/\/toposuranos.com\/material\/zh\/\u5b8c\u6574\u57df\u4e0e\u6574\u6570\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-05-09T13:00:21+00:00","article_modified_time":"2025-03-03T22:08:31+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570","twitter_description":"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570","datePublished":"2021-05-09T13:00:21+00:00","dateModified":"2025-03-03T22:08:31+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/"},"wordCount":799,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.jpg","articleSection":["\u4e00\u822c\u4ee3\u6570","\u6570\u5b66"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/","url":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/","name":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.jpg","datePublished":"2021-05-09T13:00:21+00:00","dateModified":"2025-03-03T22:08:31+00:00","description":"\u63a2\u7d22\u4ee3\u6570\u4e2d\u7684\u5b8c\u6574\u57df\uff0c\u5176\u6027\u8d28\u4ee5\u53ca\u5b83\u4eec\u4e0e\u6574\u6570\u7684\u5173\u7cfb\uff0c\u5e76\u901a\u8fc7\u8bc1\u660e\u548c\u7ec3\u4e60\u52a0\u6df1\u7406\u89e3\u3002","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/03\/algebrageneral.jpg","width":1792,"height":1024,"caption":"Dominios de Integridad, Integrity Domains, Dom\u00ednios de Integridade, \u6574\u6570\u57df, \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629, \u0905\u0916\u0902\u0921\u0924\u093e \u0921\u094b\u092e\u0947\u0928, \u0414\u043e\u043c\u0435\u043d\u044b \u0446\u0435\u043b\u043e\u0441\u0442\u043d\u043e\u0441\u0442\u0438, Domaines d'Int\u00e9grit\u00e9"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/zh\/%e5%ae%8c%e6%95%b4%e5%9f%9f%e4%b8%8e%e6%95%b4%e6%95%b0\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u5b8c\u6574\u57df\u4e0e\u6574\u6570"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/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":"https:\/\/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":"https:\/\/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":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/32334","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=32334"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/32334\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/32317"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=32334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=32334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=32334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}