{"id":25815,"date":"2021-03-20T00:00:00","date_gmt":"2021-03-20T00:00:00","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25815"},"modified":"2025-03-02T19:58:28","modified_gmt":"2025-03-02T19:58:28","slug":"%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/","title":{"rendered":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\"><center><\/p>\n<h1>\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u53ca\u5176\u987a\u5e8f\u5173\u7cfb<\/h1>\n<p style=\"text-align:center;\"><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u4e86\u89e3\u81ea\u7136\u6570\u53ca\u5176\u57fa\u672c\u8fd0\u7b97\uff0c\u4ece\u52a0\u6cd5\u3001\u4e58\u6cd5\u548c\u4e58\u65b9\u7684\u8d77\u6e90\u548c\u6027\u8d28\u5f00\u59cb\uff0c\u4e0e\u76ae\u4e9a\u8bfa\u516c\u7406\u76f8\u5173\u3002\u6211\u4eec\u5c06\u68c0\u67e5\u5173\u952e\u6027\u8d28\uff0c\u5982\u4ea4\u6362\u6027\u3001\u7ed3\u5408\u6027\u3001\u5206\u914d\u6027\u4ee5\u53ca\u7b80\u5316\u548c\u9006\u8fd0\u7b97\u89c4\u5219\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\u6765\u8bc1\u660e\u5b9a\u7406\u548c\u6027\u8d28\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5c06\u5206\u6790\u81ea\u7136\u6570\u4e4b\u95f4\u7684\u987a\u5e8f\u5173\u7cfb\uff0c\u5305\u62ec\u4e09\u6bb5\u8bba\u548c\u4f20\u9012\u6027\u3001\u5355\u8c03\u6027\u7684\u6027\u8d28\uff0c\u5e76\u901a\u8fc7\u5b9e\u8df5\u7ec3\u4e60\u5e94\u7528\u8fd9\u4e9b\u6982\u5ff5\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u9006\u8fd0\u7b97\uff08\u51cf\u6cd5\u548c\u9664\u6cd5\uff09\u5e76\u63a2\u7d22\u81ea\u7136\u6570\u7684\u4e58\u65b9\u53ca\u5176\u6027\u8d28\u3002\n<\/p>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u8fd9\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<p style=\"text-align:justify;\">\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90\u548c\u6027\u8d28\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u81ea\u7136\u6570\u8fd0\u7b97\u7684\u6027\u8d28\uff0c\u5982\u4ea4\u6362\u6027\u3001\u7ed3\u5408\u6027\u3001\u5206\u914d\u6027\u4ee5\u53ca\u7b80\u5316\u548c\u9006\u8fd0\u7b97\u89c4\u5219\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u6570\u5b66\u5f52\u7eb3\u6cd5\u6765\u8bc1\u660e\u7b80\u5355\u7684\u6027\u8d28\u548c\u5b9a\u7406\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u81ea\u7136\u6570\u7684\u987a\u5e8f\u6027\u8d28\uff0c\u5982\u4e09\u6bb5\u8bba\u4ee5\u53ca\u4f20\u9012\u6027\u548c\u5355\u8c03\u6027\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u76ee\u5f55<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90<\/a><br \/>\n<a href=\"#2\">\u81ea\u7136\u6570\u8fd0\u7b97\u8bf1\u5bfc\u7684\u987a\u5e8f<\/a><br \/>\n<a href=\"#3\">\u81ea\u7136\u6570\u7684\u9006\u8fd0\u7b97\uff1a\u51cf\u6cd5\u548c\u9664\u6cd5<\/a><br \/>\n<a href=\"#4\">\u81ea\u7136\u6570\u7684\u4e58\u65b9<\/a><br \/>\n<a href=\"#5\">\u63d0\u51fa\u548c\u89e3\u51b3\u7684\u95ee\u9898<\/a>\n<\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/jKD71TjMC4s\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u5c3d\u7ba1\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u662f\u4f17\u6240\u5468\u77e5\u7684\uff0c\u4f46\u6211\u4eec\u9700\u8981\u7528\u66f4\u52a0\u201c\u6570\u5b66\u7684\u65b9\u5f0f\u201d\u6765\u7efc\u5408\u8fd9\u4e9b\u77e5\u8bc6\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u590d\u4e60\u81ea\u7136\u6570\u7684\u52a0\u6cd5\u3001\u4e58\u6cd5\u548c\u4e58\u65b9\u8fd0\u7b97\u53ca\u5176\u6027\u8d28\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90<\/h2>\n<h3>\u52a0\u6cd5\u8fd0\u7b97<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=49s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u6211\u4eec\u5728\u5173\u4e8e<\/strong><\/span><\/a> <a href=\"http:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e4%b8%8epeano%e5%85%ac%e7%90%86\/\" rel=\"noopener\" target=\"_blank\"><strong>\u81ea\u7136\u6570\u548c\u76ae\u4e9a\u8bfa\u516c\u7406\u7684\u8bfe\u7a0b\u4e2d\u590d\u4e60\u4e86\u52a0\u6cd5\u8fd0\u7b97\u7684\u8d77\u6e90\uff0c<\/strong><\/a>\u56e0\u4e3a\u81ea\u7136\u6570\u7684\u540e\u7ee7\u4e5f\u53ef\u4ee5\u8fd9\u6837\u8868\u793a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">S(n) = n+1<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6b63\u5982\u6211\u4eec\u6240\u8bf4\u7684\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">2=S(1), 3=S(2), 4=S(3), \\cdots <\/span><\/bdi> \u7b49\u7b49\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u52a0\u6cd5\u89e3\u91ca\u4e3a\u8fde\u7eed\u7684\u540e\u7ee7\u64cd\u4f5c\u3002<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">n+1 =S(n),<\/span><\/bdi><\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">n+2 =S(S(n)),<\/span><\/bdi><\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">n+3 =S(S(S(n))),<\/span><\/bdi><\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u603b\u7684\u6765\u8bf4\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">n+m = \\underbrace{S(S(\\cdots S(}_{m\\;\u6b21} n)\\cdots)) <\/span><\/bdi><\/p>\n<h4>\u52a0\u6cd5\u7684\u6027\u8d28<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{N},<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=131s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u90a3\u4e48\u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u6211\u4eec\u90fd\u77e5\u9053\u7684\u52a0\u6cd5\u6027\u8d28\uff1a<\/span><\/strong><\/a><\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u4ea4\u6362\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a+b=b+a<\/span><\/bdi><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u7ed3\u5408\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a+b+c=(a+b)+c=a+(b+c)<\/span><\/bdi><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u7b80\u5316<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a+b=a+c \\leftrightarrow b=c <\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u6240\u6709\u8fd9\u4e9b\u6027\u8d28\u90fd\u53ef\u4ee5\u901a\u8fc7\u5f52\u7eb3\u6cd5\u8bc1\u660e\uff0c\u4f46\u6211\u4eec\u4e0d\u4f1a\u5728\u8fd9\u91cc\u5c55\u5f00\u3002\u4e0d\u8fc7\uff0c\u6211\u9f13\u52b1\u4f60\u5c1d\u8bd5\u8fd9\u6837\u505a\uff0c\u4f5c\u4e3a\u7ec3\u4e60\u5f52\u7eb3\u6cd5\u6280\u5de7\u7684\u4e00\u79cd\u65b9\u5f0f\u3002<\/p>\n<h3>\u4e58\u6cd5\u8fd0\u7b97<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=230s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7c7b\u4f3c\u5730\uff0c\u81ea\u7136\u6570\u7684\u4e58\u6cd5<\/span><\/strong><\/a>\u88ab\u5b9a\u4e49\u4e3a\u52a0\u6cd5\u7684\u8fde\u7eed\u5e94\u7528\u3002\u56e0\u6b64\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">n\\cdot m = \\underbrace{n+ n+ \\cdots + n}_{m\\;\u6b21}<\/span><\/bdi><\/p>\n<h4>\u4e58\u6cd5\u7684\u6027\u8d28<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=251s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u540c\u6837\u5730<\/span><\/strong><\/a>\u53ef\u4ee5\u5f97\u51fa\u5b83\u7684\u6027\u8d28\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u4ea4\u6362\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">ab=ba<\/span><\/bdi><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u7ed3\u5408\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">abc=(ab)c=a(bc)<\/span><\/bdi><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u7b80\u5316<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">ab=ac \\leftrightarrow b=c <\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u6b64\u5916\uff0c\u6839\u636e\u4e58\u6cd5\u7684\u5b9a\u4e49\uff0c\u201c1\u201d\u5728\u81ea\u7136\u6570\u4e2d\u83b7\u5f97\u4e86\u4f7f\u5176\u6210\u4e3a<strong>\u5355\u4f4d<\/strong>\u7684\u7279\u6027\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u5355\u4f4d<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">1a=a=a1<\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u52a0\u6cd5\u548c\u4e58\u6cd5\u7684\u7ec4\u5408<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u5f53\u52a0\u6cd5\u548c\u4e58\u6cd5\u7ed3\u5408\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u52a0\u6cd5\u76f8\u5bf9\u4e8e\u4e58\u6cd5\u7684\u5206\u914d\u6027\u8d28<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td><strong>\u5206\u914d\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a(b+c)=ab+ac<\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u8fd0\u7b97\u5f15\u5bfc\u7684\u987a\u5e8f<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u6211\u4eec\u590d\u4e60\u7684\u52a0\u6cd5\u548c\u4e58\u6cd5\u8fd0\u7b97\u4e2d\uff0c\u53ef\u4ee5\u5728\u81ea\u7136\u6570\u4e2d\u5f15\u5bfc\u51fa\u4e00\u79cd\u987a\u5e8f\u5173\u7cfb\uff0c\u901a\u8fc7\u4ee5\u4e0b\u5b9a\u4e49\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; color: #000000;\"><strong><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u5c0f\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b := (\\exists k \\in \\mathbb{N}) (a + k = b)<\/span><\/bdi><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; color: #000000;\"><strong><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u5927\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b := (\\exists k \\in \\mathbb{N}) (a = b + k)<\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u81ea\u7136\u6570\u7684\u987a\u5e8f\u6027\u8d28<\/h3>\n<h4>\u4e09\u6bb5\u8bba\u6cd5\u5219<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=513s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff0c\u53ea\u4f1a\u53d1\u751f\u4ee5\u4e0b\u4e09\u79cd\u60c5\u51b5\u4e2d\u7684\u4e00\u79cd\uff1a<\/strong><\/span><\/a><\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\lt b<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">a = b<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b<\/span><\/bdi><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u4f8b\u5982<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u4e0d\u5c0f\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\uff0c\u5219\u5fc5\u5b9a\u53d1\u751f\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5\u4e4b\u4e00\uff1a\u8981\u4e48<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a=b<\/span><\/bdi>\uff0c\u8981\u4e48<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b<\/span><\/bdi>\uff0c\u5373\u5927\u4e8e\u6216\u7b49\u4e8e\uff0c\u53ef\u4ee5\u5199\u4f5c\uff1a<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\geq b.<\/span><\/bdi> \u540c\u7406\uff0c\u5f53\u5c0f\u4e8e\u6216\u7b49\u4e8e\u65f6\uff0c\u53ef\u4ee5\u5199\u4f5c\uff1a<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\leq b.<\/span><\/bdi>\u3002<\/p>\n<h4>\u4f20\u9012\u6027\u8d28<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">a,b<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=625s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u662f\u4efb\u4f55\u81ea\u7136\u6570\uff0c\u5219\u6709\uff1a<\/strong><\/span><\/a><\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">[(a\\lt b) \\wedge (b\\lt c)] \\rightarrow (a\\lt c)<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u540c\u7406\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">[(a\\gt b) \\wedge (b\\gt c)] \\rightarrow (a\\gt c)<\/span><\/bdi><\/p>\n<h4>\u5355\u8c03\u6027\u8d28<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u5bf9\u4e8e\u52a0\u6cd5\u548c\u4e58\u6cd5\u90fd\u5b58\u5728\u5355\u8c03\u6027\u8d28\uff0c\u5373\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; color: #000000;\"><strong>\u52a0\u6cd5\u7684\u5355\u8c03\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a\\lt b) \\leftrightarrow (a+c \\lt b+c) <\/span><\/bdi><bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a\\gt b) \\leftrightarrow (a+c \\gt b+c)<\/span><\/bdi><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; color: #000000;\"><strong>\u4e58\u6cd5\u7684\u5355\u8c03\u6027<\/strong><br \/>\n<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a\\lt b) \\leftrightarrow (a c \\lt b c) <\/span><\/bdi><bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a\\gt b) \\leftrightarrow (a c \\gt b c)<\/span><\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u7684\u9006\u8fd0\u7b97\uff1a\u51cf\u6cd5\u548c\u9664\u6cd5<\/h2>\n<h3>\u81ea\u7136\u6570\u7684\u51cf\u6cd5<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{N}<\/span><\/bdi>\uff0c<a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=782s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u8bf4<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u4e4b\u95f4\u7684\u5dee\uff08\u6309\u8be5\u987a\u5e8f\uff09\uff0c\u5199\u4f5c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a-b<\/span><\/bdi>\uff0c\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5b9a\u4e49<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">a-b=c \\leftrightarrow a= b+c<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6b63\u5982\u6211\u4eec\u6240\u89c1\uff0c\u8fd9\u79cd\u5173\u7cfb\u53ea\u6709\u5728 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b<\/span><\/bdi> \u65f6\u624d\u6210\u7acb\uff0c\u56e0\u4e3a\u5982\u679c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\leq b<\/span><\/bdi>\uff0c\u5219\u4e0d\u5b58\u5728\u53ef\u4ee5\u6ee1\u8db3\u8fd9\u79cd\u5173\u7cfb\u7684 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\in \\mathbb{N}<\/span><\/bdi>\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u51cf\u6cd5\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4f17\u6240\u5468\u77e5\u7684\u89c4\u5219\uff1a\u00bb\u7b49\u5f0f\u4e00\u4fa7\u7684\u52a0\u6cd5\u53ef\u4ee5\u53d8\u4e3a\u53e6\u4e00\u4fa7\u7684\u51cf\u6cd5\uff0c\u53cd\u4e4b\u4ea6\u7136\u00bb\u3002<\/p>\n<h3>\u81ea\u7136\u6570\u7684\u9664\u6cd5<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{N}<\/span><\/bdi>\uff0c<a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=917s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u6211\u4eec\u8bf4<\/strong><\/span><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u4e4b\u95f4\u7684\u9664\u6cd5\uff08\u6309\u8be5\u987a\u5e8f\uff09\uff0c\u5199\u4f5c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\/b<\/span><\/bdi>\uff0c\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5b9a\u4e49<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\/b=c \\leftrightarrow a= bc<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e\u9664\u6cd5\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u89c4\u5219\uff1a\u00bb\u7b49\u5f0f\u4e00\u4fa7\u7684\u4e58\u6cd5\u53ef\u4ee5\u53d8\u4e3a\u53e6\u4e00\u4fa7\u7684\u9664\u6cd5\uff0c\u53cd\u4e4b\u4ea6\u7136\u00bb\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5c31\u50cf\u8981\u5b58\u5728\u51cf\u6cd5 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a - b<\/span><\/bdi> \u5fc5\u987b\u6ee1\u8db3 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b<\/span><\/bdi> \u4e00\u6837\uff0c\u8981\u5b58\u5728\u9664\u6cd5 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\/b<\/span><\/bdi>\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u5fc5\u987b\u80fd\u88ab <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u00ab\u6574\u9664\u00bb\u3002\u6211\u4eec\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u8868\u793a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u53ef\u4ee5\u88ab <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u6574\u9664 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\; :=a|b \\; := \\; (\\exists k \\in \\mathbb{N})(a = kb)<\/span><\/bdi><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u7684\u4e58\u65b9<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1020s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>\u4f7f\u7528\u81ea\u7136\u6570\u53ef\u4ee5\u5b9a\u4e49\u4e58\u65b9\u3002<\/strong> <\/span><\/a>\u5c06\u4e00\u4e2a\u81ea\u7136\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">b,<\/span> \u6211\u4eec\u79f0\u4e4b\u4e3a\u5e95\u6570\uff0c\u4e58\u4ee5\u53e6\u4e00\u4e2a\u81ea\u7136\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">n,<\/span> \u6211\u4eec\u79f0\u4e4b\u4e3a\u6307\u6570\uff0c\u610f\u5473\u7740\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u4e58\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u6b21\u3002\u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><bdi><span class=\"katex-eq\" data-katex-display=\"false\">b^n = \\underbrace{bb\\cdots b}_{n\\;\u6b21}<\/span><\/bdi><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c <bdi><span class=\"katex-eq\" data-katex-display=\"false\">a,b,n,m\\in\\mathbb{N},<\/span><\/bdi> \u901a\u8fc7\u5f52\u7eb3\u6cd5\uff08\u53cc\u91cd\uff09\u53ef\u4ee5\u8bc1\u660e\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle b^nb^m=b^{n+m}<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{b^n}{b^m} = b^{n-m},<\/span><\/bdi> \u53ea\u8981 <bdi><span class=\"katex-eq\" data-katex-display=\"false\">n\\lt m<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle (ab)^n=a^nb^n<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{a}{b}\\right)^n = \\frac{a^n}{b^n}<\/span><\/bdi><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle (b^n)^m=b^{nm}<\/span><\/bdi><\/li>\n<\/ol>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u63d0\u51fa\u548c\u89e3\u51b3\u7684\u95ee\u9898<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u6211\u4eec\u5728\u8fd9\u91cc\u5c55\u793a\u7684\u6240\u6709\u6027\u8d28\u90fd\u53ef\u4ee5\u901a\u8fc7\u6570\u5b66\u5f52\u7eb3\u6cd5\uff08\u5355\u4e00\u6216\u53cc\u91cd\uff09\u6765\u8bc1\u660e\uff0c\u4f46\u6211\u6ca1\u6709\u8be6\u7ec6\u5c55\u5f00\uff0c\u56e0\u4e3a\u5bf9\u4e8e\u8fd9\u4e9b\u76f4\u89c2\u7684\u7ed3\u679c\u6765\u8bf4\uff0c\u8bc1\u660e\u8fc7\u7a0b\u4e0d\u5fc5\u8981\u5730\u8fc7\u957f\u3002\u7136\u800c\uff0c\u8ddf\u968f\u8fd9\u4e9b\u8bfe\u7a0b\u7684\u4eba\u53ef\u4ee5\u5c1d\u8bd5\u4f5c\u4e3a\u7ec3\u4e60\u6765\u8fdb\u884c\u8fd9\u4e9b\u8bc1\u660e\u3002<strong>[\u4ec5\u63d0\u51fa]<\/strong><\/li>\n<li><bdi><span class=\"katex-eq\" data-katex-display=\"false\">b^{n^m}<\/span><\/bdi>\uff08\u5b9a\u4e49\u4e3a<bdi><span class=\"katex-eq\" data-katex-display=\"false\">b^{(n^m)})<\/span><\/bdi>\u4e0e<bdi><span class=\"katex-eq\" data-katex-display=\"false\">(b^n)^m<\/span><\/bdi>\u662f\u4e00\u6837\u7684\u5417\uff1f<a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1298s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89e3\u51b3\u65b9\u6848]<\/span><\/strong><\/a><\/li>\n<li>\u4f7f\u7528\u6211\u4eec\u770b\u5230\u7684\u6027\u8d28\u6765\u9a8c\u8bc1\u4ee5\u4e0b\u7b49\u5f0f\uff1a<br \/>\na) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a+b)(c+d) = ac+ad+bc+bd<\/span><\/bdi><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1556s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a><\/br><br \/>\nb) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a+b)(c-d) = ac-ad+bc-bd,<\/span><\/bdi>\uff1b\u5982\u679c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\gt d<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1660s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a> <\/br><br \/>\nc) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)(c-d) = ac-ad-bc+bd,<\/span><\/bdi>\uff1b\u5982\u679c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">a\\gt b<\/span><\/bdi>\u548c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\gt d<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1730s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a>&nbsp;<\/li>\n<li>\u8bc1\u660e\uff1a<\/br><br \/>\na) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a+b)^2 = a^2 + 2ab + b^2<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1903s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a> <\/br><br \/>\nb) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)^2 = a^2 - 2ab + b^2<\/span><\/bdi>\uff1b\u5982\u679c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\gt d<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1953s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a> <\/br><br \/>\nc) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a+b)(a-b) = a^2-b^2<\/span><\/bdi>\uff1b\u5982\u679c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\gt d<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=1978s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a> <\/br><br \/>\nd) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a+b)^3 = a^3 + 3a^2b+3ab^2+b^3<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=2008s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a><\/br><br \/>\ne) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)^3 = a^3 - 3a^2b+3ab^2-b^3<\/span><\/bdi>\uff1b\u5982\u679c<bdi><span class=\"katex-eq\" data-katex-display=\"false\">c\\gt d<\/span><\/bdi><a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=2124s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"> <strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a><\/p>\n<p>&nbsp;<\/li>\n<li>\u901a\u8fc7\u5b8c\u5168\u5f52\u7eb3\u6cd5\u8bc1\u660e\u4ee5\u4e0b\u6027\u8d28\uff1a<\/br><br \/>\na) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">1+2+3+4+\\cdots+n = \\displaystyle \\frac{n(n+1)}{2}<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=2328s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a> <\/br><br \/>\nb) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">1^2+2^2+3^2+4^2+\\cdots+n^2 = \\displaystyle \\frac{n(n+1)(2n+1)}{6}<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=2505s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a><\/br><br \/>\nc) <bdi><span class=\"katex-eq\" data-katex-display=\"false\">1^3+2^3+3^3+4^3+\\cdots+n^3 = \\displaystyle \\frac{n^2(n+1)^2}{4}<\/span><\/bdi> <a href=\"https:\/\/www.youtube.com\/watch?v=jKD71TjMC4s&amp;t=2972s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span><\/a>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u53ca\u5176\u987a\u5e8f\u5173\u7cfb \u6458\u8981\uff1a \u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u4e86\u89e3\u81ea\u7136\u6570\u53ca\u5176\u57fa\u672c\u8fd0\u7b97\uff0c\u4ece\u52a0\u6cd5\u3001\u4e58\u6cd5\u548c\u4e58\u65b9\u7684\u8d77\u6e90\u548c\u6027\u8d28\u5f00\u59cb\uff0c\u4e0e\u76ae\u4e9a\u8bfa\u516c\u7406\u76f8\u5173\u3002\u6211\u4eec\u5c06\u68c0\u67e5\u5173\u952e\u6027\u8d28\uff0c\u5982\u4ea4\u6362\u6027\u3001\u7ed3\u5408\u6027\u3001\u5206\u914d\u6027\u4ee5\u53ca\u7b80\u5316\u548c\u9006\u8fd0\u7b97\u89c4\u5219\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\u6765\u8bc1\u660e\u5b9a\u7406\u548c\u6027\u8d28\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5c06\u5206\u6790\u81ea\u7136\u6570\u4e4b\u95f4\u7684\u987a\u5e8f\u5173\u7cfb\uff0c\u5305\u62ec\u4e09\u6bb5\u8bba\u548c\u4f20\u9012\u6027\u3001\u5355\u8c03\u6027\u7684\u6027\u8d28\uff0c\u5e76\u901a\u8fc7\u5b9e\u8df5\u7ec3\u4e60\u5e94\u7528\u8fd9\u4e9b\u6982\u5ff5\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u9006\u8fd0\u7b97\uff08\u51cf\u6cd5\u548c\u9664\u6cd5\uff09\u5e76\u63a2\u7d22\u81ea\u7136\u6570\u7684\u4e58\u65b9\u53ca\u5176\u6027\u8d28\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u8fd9\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u7406\u89e3\u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90\u548c\u6027\u8d28\u3002 \u5e94\u7528\u81ea\u7136\u6570\u8fd0\u7b97\u7684\u6027\u8d28\uff0c\u5982\u4ea4\u6362\u6027\u3001\u7ed3\u5408\u6027\u3001\u5206\u914d\u6027\u4ee5\u53ca\u7b80\u5316\u548c\u9006\u8fd0\u7b97\u89c4\u5219\u3002 \u5e94\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\u6765\u8bc1\u660e\u7b80\u5355\u7684\u6027\u8d28\u548c\u5b9a\u7406\u3002 \u5206\u6790\u81ea\u7136\u6570\u7684\u987a\u5e8f\u6027\u8d28\uff0c\u5982\u4e09\u6bb5\u8bba\u4ee5\u53ca\u4f20\u9012\u6027\u548c\u5355\u8c03\u6027\u3002 \u5185\u5bb9\u76ee\u5f55: \u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90 \u81ea\u7136\u6570\u8fd0\u7b97\u8bf1\u5bfc\u7684\u987a\u5e8f \u81ea\u7136\u6570\u7684\u9006\u8fd0\u7b97\uff1a\u51cf\u6cd5\u548c\u9664\u6cd5 \u81ea\u7136\u6570\u7684\u4e58\u65b9 \u63d0\u51fa\u548c\u89e3\u51b3\u7684\u95ee\u9898 \u5c3d\u7ba1\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u662f\u4f17\u6240\u5468\u77e5\u7684\uff0c\u4f46\u6211\u4eec\u9700\u8981\u7528\u66f4\u52a0\u201c\u6570\u5b66\u7684\u65b9\u5f0f\u201d\u6765\u7efc\u5408\u8fd9\u4e9b\u77e5\u8bc6\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u590d\u4e60\u81ea\u7136\u6570\u7684\u52a0\u6cd5\u3001\u4e58\u6cd5\u548c\u4e58\u65b9\u8fd0\u7b97\u53ca\u5176\u6027\u8d28\u3002 \u81ea\u7136\u6570\u57fa\u672c\u8fd0\u7b97\u7684\u8d77\u6e90 \u52a0\u6cd5\u8fd0\u7b97 \u6211\u4eec\u5728\u5173\u4e8e \u81ea\u7136\u6570\u548c\u76ae\u4e9a\u8bfa\u516c\u7406\u7684\u8bfe\u7a0b\u4e2d\u590d\u4e60\u4e86\u52a0\u6cd5\u8fd0\u7b97\u7684\u8d77\u6e90\uff0c\u56e0\u4e3a\u81ea\u7136\u6570\u7684\u540e\u7ee7\u4e5f\u53ef\u4ee5\u8fd9\u6837\u8868\u793a\uff1a \u6b63\u5982\u6211\u4eec\u6240\u8bf4\u7684\uff0c \u7b49\u7b49\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u52a0\u6cd5\u89e3\u91ca\u4e3a\u8fde\u7eed\u7684\u540e\u7ee7\u64cd\u4f5c\u3002 \u603b\u7684\u6765\u8bf4\uff1a \u52a0\u6cd5\u7684\u6027\u8d28 \u5982\u679c \u90a3\u4e48\u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u6211\u4eec\u90fd\u77e5\u9053\u7684\u52a0\u6cd5\u6027\u8d28\uff1a \u4ea4\u6362\u6027 \u7ed3\u5408\u6027 \u7b80\u5316 \u6240\u6709\u8fd9\u4e9b\u6027\u8d28\u90fd\u53ef\u4ee5\u901a\u8fc7\u5f52\u7eb3\u6cd5\u8bc1\u660e\uff0c\u4f46\u6211\u4eec\u4e0d\u4f1a\u5728\u8fd9\u91cc\u5c55\u5f00\u3002\u4e0d\u8fc7\uff0c\u6211\u9f13\u52b1\u4f60\u5c1d\u8bd5\u8fd9\u6837\u505a\uff0c\u4f5c\u4e3a\u7ec3\u4e60\u5f52\u7eb3\u6cd5\u6280\u5de7\u7684\u4e00\u79cd\u65b9\u5f0f\u3002 \u4e58\u6cd5\u8fd0\u7b97 \u7c7b\u4f3c\u5730\uff0c\u81ea\u7136\u6570\u7684\u4e58\u6cd5\u88ab\u5b9a\u4e49\u4e3a\u52a0\u6cd5\u7684\u8fde\u7eed\u5e94\u7528\u3002\u56e0\u6b64\u6211\u4eec\u6709\uff1a \u4e58\u6cd5\u7684\u6027\u8d28 \u540c\u6837\u5730\u53ef\u4ee5\u5f97\u51fa\u5b83\u7684\u6027\u8d28\uff1a \u4ea4\u6362\u6027 \u7ed3\u5408\u6027 \u7b80\u5316 \u6b64\u5916\uff0c\u6839\u636e\u4e58\u6cd5\u7684\u5b9a\u4e49\uff0c\u201c1\u201d\u5728\u81ea\u7136\u6570\u4e2d\u83b7\u5f97\u4e86\u4f7f\u5176\u6210\u4e3a\u5355\u4f4d\u7684\u7279\u6027\uff1a \u5355\u4f4d \u52a0\u6cd5\u548c\u4e58\u6cd5\u7684\u7ec4\u5408 \u5f53\u52a0\u6cd5\u548c\u4e58\u6cd5\u7ed3\u5408\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u52a0\u6cd5\u76f8\u5bf9\u4e8e\u4e58\u6cd5\u7684\u5206\u914d\u6027\u8d28 \u5206\u914d\u6027 \u81ea\u7136\u6570\u8fd0\u7b97\u5f15\u5bfc\u7684\u987a\u5e8f \u4ece\u6211\u4eec\u590d\u4e60\u7684\u52a0\u6cd5\u548c\u4e58\u6cd5\u8fd0\u7b97\u4e2d\uff0c\u53ef\u4ee5\u5728\u81ea\u7136\u6570\u4e2d\u5f15\u5bfc\u51fa\u4e00\u79cd\u987a\u5e8f\u5173\u7cfb\uff0c\u901a\u8fc7\u4ee5\u4e0b\u5b9a\u4e49\uff1a \u5c0f\u4e8e \u5927\u4e8e \u81ea\u7136\u6570\u7684\u987a\u5e8f\u6027\u8d28 \u4e09\u6bb5\u8bba\u6cd5\u5219 \u4ece\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff0c\u53ea\u4f1a\u53d1\u751f\u4ee5\u4e0b\u4e09\u79cd\u60c5\u51b5\u4e2d\u7684\u4e00\u79cd\uff1a \u5982\u679c\u4f8b\u5982\u4e0d\u5c0f\u4e8e\uff0c\u5219\u5fc5\u5b9a\u53d1\u751f\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5\u4e4b\u4e00\uff1a\u8981\u4e48\uff0c\u8981\u4e48\uff0c\u5373\u5927\u4e8e\u6216\u7b49\u4e8e\uff0c\u53ef\u4ee5\u5199\u4f5c\uff1a \u540c\u7406\uff0c\u5f53\u5c0f\u4e8e\u6216\u7b49\u4e8e\u65f6\uff0c\u53ef\u4ee5\u5199\u4f5c\uff1a\u3002 \u4f20\u9012\u6027\u8d28 \u5982\u679c\u548c \u662f\u4efb\u4f55\u81ea\u7136\u6570\uff0c\u5219\u6709\uff1a \u540c\u7406\uff1a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25803,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":15,"footnotes":""},"categories":[1035,591,575],"tags":[],"class_list":["post-25815","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1035","category-591","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027\" \/>\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\/\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\" \/>\n<meta property=\"og:description\" content=\"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/zh\/\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\/\" \/>\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=\"2021-03-20T00:00:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-03-02T19:58:28+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\" \/>\n<meta name=\"twitter:description\" content=\"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\",\"datePublished\":\"2021-03-20T00:00:00+00:00\",\"dateModified\":\"2025-03-02T19:58:28+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/\"},\"wordCount\":606,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/OPERACIONES.jpg\",\"articleSection\":[\"\u4e00\u822c\u4ee3\u6570\",\"\u4ee3\u6570\u4e0e\u51e0\u4f55\",\"\u6570\u5b66\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/\",\"name\":\"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/OPERACIONES.jpg\",\"datePublished\":\"2021-03-20T00:00:00+00:00\",\"dateModified\":\"2025-03-02T19:58:28+00:00\",\"description\":\"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/OPERACIONES.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/OPERACIONES.jpg\",\"width\":1792,\"height\":1024,\"caption\":\"Operaciones con n\u00fameros naturales\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\"}]},{\"@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":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97 - toposuranos.com\/material","description":"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027","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\/\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\/","og_locale":"es_ES","og_type":"article","og_title":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97","og_description":"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027","og_url":"https:\/\/toposuranos.com\/material\/zh\/\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-20T00:00:00+00:00","article_modified_time":"2025-03-02T19:58:28+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97","twitter_description":"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"2 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97","datePublished":"2021-03-20T00:00:00+00:00","dateModified":"2025-03-02T19:58:28+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/"},"wordCount":606,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.jpg","articleSection":["\u4e00\u822c\u4ee3\u6570","\u4ee3\u6570\u4e0e\u51e0\u4f55","\u6570\u5b66"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/","url":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/","name":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.jpg","datePublished":"2021-03-20T00:00:00+00:00","dateModified":"2025-03-02T19:58:28+00:00","description":"\u5173\u4e8e\u81ea\u7136\u6570\u7684\u6240\u6709\u8fd0\u7b97\u548c\u987a\u5e8f\u5173\u7cfb\u3001\u76ae\u4e9a\u8bfa\u516c\u7406\u3001\u5f52\u7eb3\u6cd5\u3001\u4e09\u6bb5\u8bba\u548c\u5355\u8c03\u6027","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/12\/OPERACIONES.jpg","width":1792,"height":1024,"caption":"Operaciones con n\u00fameros naturales"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/zh\/%e8%87%aa%e7%84%b6%e6%95%b0%e5%8f%8a%e5%85%b6%e9%a1%ba%e5%ba%8f%e5%85%b3%e7%b3%bb%e7%9a%84%e8%bf%90%e7%ae%97\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u81ea\u7136\u6570\u53ca\u5176\u987a\u5e8f\u5173\u7cfb\u7684\u8fd0\u7b97"}]},{"@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\/25815","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=25815"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/25815\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/25803"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=25815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=25815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=25815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}