\u6570\u5b57\u96c6\u7684\u521d\u6b65\u4e86\u89e3 – ToposUranos.com<\/title> <\/head> <body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6570\u5b57\u96c6\u521d\u63a2\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570<\/h1>\n<\/center><\/p>\n\u6458\u8981\uff1a<\/strong><\/br>\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u7d22\u5982\u4f55\u4f7f\u7528\u81ea\u7136\u6570\u4f5c\u4e3a\u6784\u5efa\u5176\u4ed6\u6570\u5b57\u96c6\u7684\u57fa\u7840\uff0c\u4ee5\u89e3\u51b3\u67d0\u4e9b\u64cd\u4f5c\u9650\u5236\u3002\u6211\u4eec\u5c06\u4ece\u6574\u6570\u5f00\u59cb\uff0c\u5b83\u4eec\u4f7f\u6211\u4eec\u80fd\u591f\u5e7f\u6cdb\u5730\u6267\u884c\u51cf\u6cd5\u3002\u7136\u540e\uff0c\u6211\u4eec\u5c06\u8fdb\u4e00\u6b65\u7814\u7a76\u6709\u7406\u6570\uff0c\u5b83\u4eec\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u5b8c\u6574\u7684\u9664\u6cd5\u5de5\u5177\u3002\u968f\u540e\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u4e86\u89e3\u5b9e\u6570\uff0c\u4ee5\u4fbf\u80fd\u591f\u5904\u7406 n-\u6b21\u65b9\u6839\uff0c\u5e76\u63d0\u53ca\u5982\u4f55\u5f15\u5165\u590d\u6570\u4ee5\u5904\u7406\u7279\u5b9a\u573a\u666f\u4e2d\u7684 n-\u6b21\u65b9\u6839\u3002\u901a\u8fc7\u8fd9\u4e9b\u53d1\u5c55\uff0c\u5c06\u7406\u89e3\u6bcf\u4e2a\u65b0\u7684\u6570\u5b57\u96c6\u662f\u5982\u4f55\u51fa\u73b0\u7684\uff0c\u4ee5\u89e3\u51b3\u524d\u4e00\u4e2a\u96c6\u5408\u4e2d\u56fa\u6709\u7684\u95ee\u9898\u3002<\/em><\/p>\n\u5b66\u4e60\u76ee\u6807<\/u>:<\/strong> \u5728\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol>\n<li>\u8bc6\u522b<\/strong>\u81ea\u7136\u6570\u3001\u6574\u6570\u548c\u6709\u7406\u6570\u7684\u57fa\u672c\u5c5e\u6027\u3002<\/li>\n<li>\u89e3\u91ca<\/strong>\u5728\u4ece\u4e00\u4e2a\u6570\u5b57\u96c6\u8fc7\u6e21\u5230\u53e6\u4e00\u4e2a\u6570\u5b57\u96c6\u65f6\u7ee7\u627f\u6216\u4fee\u6539\u7684\u57fa\u672c\u5c5e\u6027\u548c\u64cd\u4f5c\u3002<\/li>\n<li>\u6bd4\u8f83<\/strong>\u4e0d\u540c\u6570\u5b57\u96c6\u7684\u5c5e\u6027\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/li>\n<\/ol>\n\u5185\u5bb9\u7d22\u5f15<\/u><\/strong> \n<a href=\"#1\">\u7b80\u4ecb<\/a> \n<a href=\"#2\">\u81ea\u7136\u6570\u7684\u5c5e\u6027<\/a> \n<a href=\"#3\">\u4ece\u81ea\u7136\u6570\u8fc7\u6e21\u5230\u6574\u6570<\/a> \n<a href=\"#4\">\u8dc3\u5411\u6709\u7406\u6570<\/a> \n<a href=\"#5\">\u5b9e\u6570\u548c\u65e0\u7406\u6570<\/a> \n<a href=\"#6\">\u590d\u6570\uff1a\u5b9e\u6570\u7684\u4ee3\u6570\u6761\u6b3e<\/a>\n<\/p>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PfK-pIlyCj4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<a name=\"1\"><\/a><\/p>\n<h2>\u7b80\u4ecb<\/h2>\n<div class=\"content\">\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=96s\" target=\"_blank\" rel=\"noopener\">\u5b9e\u6570\uff0c\u4ee5\u53ca\u6211\u4eec\u5728\u8fd9\u8bfe\u4e2d\u5c06\u63a2\u8ba8\u7684\u5176\u4ed6\u6570\u5b57\u96c6\uff0c<\/strong><\/span><\/a>\u662f\u901a\u8fc7\u6269\u5c55\u81ea\u7136\u6570\u6765\u5f15\u5165\u7684\u3002\u4e8b\u5b9e\u662f\uff0c\u5bf9\u4e8e\u4efb\u4f55\u4e24\u4e2a\u81ea\u7136\u6570\uff0c\u5e76\u4e0d\u603b\u662f\u53ef\u4ee5\u8fdb\u884c\u51cf\u6cd5\u6216\u9664\u6cd5\u8fd0\u7b97\uff0c\u800c\u8fd9\u4e9b\u6269\u5c55\u7684\u76ee\u7684\u662f\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e<a href=\"https:\/\/toposuranos.com\/operaciones-con-numeros-naturales\/\" rel=\"noopener\" target=\"_blank\">\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u548c\u5c5e\u6027\uff0c<\/strong><\/a>\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u5c06\u7ee7\u7eed\u6784\u5efa\u6240\u6709\u5176\u4ed6\u6570\u5b57\u96c6\uff0c\u76f4\u5230\u8fbe\u5230\u5b9e\u6570\uff0c\u5e76\u4e14\u66f4\u8fdb\u4e00\u6b65\u3002<\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u7684\u5c5e\u6027<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=214s\" target=\"_blank\" rel=\"noopener\">\u5728\u5904\u7406\u81ea\u7136\u6570\u8fd0\u7b97\u65f6\uff0c<\/span><\/strong><\/a>\u6211\u4eec\u4e3b\u8981\u6307\u7684\u662f\u52a0\u6cd5\u548c\u4e58\u6cd5\uff0c\u4ee5\u53ca\u5b83\u4eec\u5404\u81ea\u7684\u9006\u8fd0\u7b97\u3002\u4e0b\u9762\u603b\u7ed3\u4e86\u8fd9\u4e9b\u5c5e\u6027\uff1a<\/p>\n\u5047\u8bbe a,b,c\\in\\mathbb{N},<\/span> \u6211\u4eec\u9a8c\u8bc1\u4e86\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>1. <\/td>\n<td>a + b = b + a<\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>2. <\/td>\n<td>a \\pm (b \\pm c) = (a\\pm b)\\pm c <\/span> (\u5728\u51cf\u6cd5\u7684\u60c5\u51b5\u4e0b\uff0c\u53ea\u6709\u5728\u5b9a\u4e49\u660e\u786e\u7684\u60c5\u51b5\u4e0b\u624d\u6709\u6548)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>3. <\/td>\n<td>a\\cdot b = b \\cdot a <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>4. <\/td>\n<td>a\\cdot(b\\cdot c)= (a\\cdot b)\\cdot c <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>5.\\;\\;\\;\\;\\;<\/span><\/td>\n<td>a\\cdot b = a \\leftrightarrow b=1 <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>6.<\/td>\n<td>\\displaystyle \\frac{a}{b}\\in\\mathbb{N} \\leftrightarrow (\\exists k\\in\\mathbb{N})(a=b\\cdot k) <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>7.<\/td>\n<td>a\\cdot(b+c)=a\\cdot b + a \\cdot c <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"3\"><\/a><\/p>\n<h2>\u4ece\u81ea\u7136\u6570\u5230\u6574\u6570\u7684\u8fc7\u6e21<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=418s\" target=\"_blank\" rel=\"noopener\">\u9996\u5148\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u6c42\u548c\u7684\u60c5\u51b5\u4e0b\uff1a<\/span><\/strong><\/a> (\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N})<\/span>\uff0c\u800c\u5bf9\u4e8e\u51cf\u6cd5\uff1a(\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N} \\leftrightarrow a\\gt b)<\/span>\u3002\u5f53\u4e24\u4e2a\u81ea\u7136\u6570 a<\/span> \u548c b<\/span> \u7684\u51cf\u6cd5\u6ca1\u6709\u610f\u4e49\u65f6\uff0c\u5373 a\\leq b<\/span>\uff0c\u95ee\u9898\u51fa\u73b0\u4e86\uff1b\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u81ea\u7136\u6570\u88ab\u6269\u5c55\u5230\u6574\u6570\u96c6\uff0c\u5176\u4e2d\u8fd9\u79cd\u6027\u8d28\u7684\u51cf\u6cd5\u5f97\u5230\u4e86\u660e\u786e\u5b9a\u4e49\u3002\u6211\u4eec\u7528\u5b57\u6bcd \\mathbb{Z}<\/span> \u8868\u793a\u8fd9\u4e2a\u65b0\u7684\u6574\u6570<\/strong>\u96c6\uff0c\u5b83\u5305\u62ec\u6240\u6709\u7684\u81ea\u7136\u6570\u3001\u5b83\u4eec\u7684\u52a0\u6cd5\u9006\u5143\u548c\u96f6\u3002<\/p>\n\\mathbb{Z} = \\{\\cdots, -3,-2,-1,0,1,2,3,\\cdots \\}<\/span>\n\u6574\u6570\u7ee7\u627f\u4e86\u6240\u6709\u81ea\u7136\u6570\u7684\u5c5e\u6027\u548c\u64cd\u4f5c\uff0c\u5e76\u5728\u7b2c\u4e8c\u4e2a\u5c5e\u6027\u4e0a\u8fdb\u884c\u4e86\u6269\u5c55\uff0c\u5f15\u5165\u4e86\u52a0\u6cd5\u9006\u5143\u548c\u52a0\u6cd5\u5355\u4f4d\u5143\u7684\u6982\u5ff5\u3002<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: left; color: #000000;\">\n<td>2*.<\/td>\n<td>a \\pm (b \\pm c) = (a\\pm b) \\pm c <\/span><\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>8.<\/td>\n<td>(\\forall a\\in\\mathbb{Z})(\\exists ! b\\in\\mathbb{Z})(a+b=0 \\leftrightarrow b=-a)<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>9.<\/td>\n<td>(\\forall a\\in\\mathbb{Z})(\\exists ! b\\in\\mathbb{Z})(a+b=a \\leftrightarrow b=0)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u5143\u7d20 b=-a<\/span> \u662f\u6211\u4eec\u6240\u8bf4\u7684 a<\/span> \u7684\u52a0\u6cd5\u9006\u5143<\/strong>\u3002<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>\u8df3\u5230\u6709\u7406\u6570<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=755s\" target=\"_blank\" rel=\"noopener\">\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u552f\u4e00\u6ca1\u6709\u6b63\u786e\u5b9a\u4e49\u7684\u64cd\u4f5c\u662f\u9664\u6cd5\u3002<\/span><\/strong><\/a> \u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5bf9\u6574\u6570\u96c6\u8fdb\u884c\u6269\u5c55\uff0c\u5f97\u5230\u6709\u7406\u6570\u96c6\uff0c\u7531\u4ee5\u4e0b\u96c6\u5408\u7ed9\u51fa\uff1a<\/p>\n\\mathbb{Q}=\\left\\{a= \\displaystyle\\frac{n}{m}\\;|\\;n,m\\in\\mathbb{Z}\\wedge m\\neq 0 \\right\\}<\/span>\n\u8fd9\u6837\u5c31\u83b7\u5f97\u4e86\u4e00\u4e2a\u65b0\u7684\u5c5e\u6027<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>10.<\/td>\n<td>(\\forall a \\in \\mathbb{Q}\\setminus\\{0\\})(\\exists ! b \\in \\mathbb{Q})<\/span> \\left[(a\\cdot b = 1) \\leftrightarrow \\left( b = \\displaystyle \\frac{1}{a} = a^{-1} \\right)\\right]<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td colspan=\"2\">\u6bcf\u4e2a\u975e\u96f6\u7684\u6709\u7406\u6570\u90fd\u6709\u4e00\u4e2a\u4e58\u6cd5\u9006\u5143\u3002 a<\/span> \u7684\u4e58\u6cd5\u9006\u5143\u662f a^{-1}<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u5bf9\u4e8e\u8fd9\u4e9b\u6570\u5b57\u3001\u64cd\u4f5c\u548c\u5c5e\u6027\uff0c\u5b9a\u4e49\u4e86\u65b0\u7684\u64cd\u4f5c\u53ca\u5176\u5c5e\u6027\u3002\u5728\u8fd9\u91cc\uff0c\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5b9a\u4e49\u6709\u7406\u6570 q<\/span> \u7684 n-\u6b21\u5e42\uff1a<\/p>\nq^n = \\underbrace{q\\cdot q \\cdot \\cdots \\cdot q}_{n\\;veces};<\/span> \u5176\u4e2d n\\in\\mathbb{N}<\/span>\nq^{-n}= \\displaystyle \\frac{1}{q^n}<\/span>\n\u8bf7\u6ce8\u610f\uff0c\u4ece\u8fd9\u91cc\u5f00\u59cb\uff0c\u53ea\u8981 q\\neq 0<\/span>\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8bf4<\/p>\nq^0 = 1<\/span>\n\u6b64\u5916\uff0c\u53ea\u8981\u51fa\u73b0\u96f6\u9664\u6cd5\uff0c\u7ed9\u5b9a\u4efb\u610f\u4e24\u4e2a\u6709\u7406\u6570 a,b<\/span> \u548c\u4e24\u4e2a\u6574\u6570 n,m<\/span>\uff0c\u5c31\u4f1a\u6ee1\u8db3\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>11.<\/td>\n<td>a^n \\cdot a^m = a^{n+m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>12.<\/td>\n<td>(a^n)^m = a^{n\\cdot m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>13.<\/td>\n<td>(a\\cdot b)^n = a^{n} \\cdot a^{m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>14.<\/td>\n<td>\\left(\\displaystyle \\frac{a}{a}\\right)^n = \\frac{a^n}{a^n} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>15.<\/td>\n<td>\\displaystyle \\frac{a^n}{a^m} = a^{n-m} = \\frac{1}{a^{m-n}} <\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"5\"><\/a><\/p>\n<h2>\u5b9e\u6570\u548c\u65e0\u7406\u6570<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1031s\" target=\"_blank\" rel=\"noopener\">\u5c31\u50cf\u51cf\u6cd5\u64cd\u4f5c\uff08\u52a0\u6cd5\u7684\u9006\u64cd\u4f5c\uff09\u548c\u9664\u6cd5<\/span><\/strong><\/a>\uff08\u4e58\u6cd5\u7684\u9006\u64cd\u4f5c\uff09\u4f7f\u5f97\u5c06\u81ea\u7136\u6570\u6269\u5c55\u5230\u6574\u6570\u548c\u6709\u7406\u6570\u6210\u4e3a\u5fc5\u8981\uff0c\u4ee5\u5f62\u6210\u660e\u786e\u5b9a\u4e49\u7684\u64cd\u4f5c\uff0c\u5e42\u8fd0\u7b97\u4e5f\u662f\u7c7b\u4f3c\u7684\u3002n<\/span>-\u6b21\u65b9\u7684\u9006\u8fd0\u7b97\u662fn<\/span>-\u6b21\u65b9\u6839\u3002<\/p>\n<h3>\u6839\u7684\u5b9a\u4e49<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1071s\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe n<\/span> \u662f\u5927\u4e8e 1 \u7684\u6574\u6570<\/span><\/strong><\/a>\uff0c\u800c p,q<\/span> \u662f\u4efb\u610f\u6709\u7406\u6570\uff0c\u6211\u4eec\u901a\u8fc7\u4ee5\u4e0b\u89c4\u5219\u5b9a\u4e49q<\/span>\u7684n<\/span>-\u6b21\u65b9\u6839\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>16.<\/td>\n<td>q=0 \\rightarrow \\sqrt[n]{q} = 0<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>17.<\/td>\n<td>q \\gt 0 \\rightarrow \\left[ \\sqrt[n]{q} = p \\leftrightarrow p^n = q \\right]<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>18.<\/td>\n<td> \\left[ q \\lt 0 \\wedge n {\\;\u662f\\;\u5947\u6570} \\right]\\rightarrow \\left[ \\sqrt[n]{q} = p \\leftrightarrow p^n = q \\right]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u603b\u7684\u6765\u8bf4\uff0cq<\/span>\u7684n<\/span>-\u6b21\u65b9\u6839\u662f\u4e00\u4e2a\u6570\u5b57p<\/span>\uff0c\u4f7f\u5f97p<\/span>\u7684n<\/span>\u6b21\u65b9\u7b49\u4e8eq<\/span>\u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5f53n=2<\/span>\u65f6\uff0c\u6211\u4eec\u7b80\u5355\u5730\u5199\\sqrt{q}<\/span>\uff0c\u800c\u4e0d\u662f\u5199\\sqrt[2]{q}<\/span>\u3002<\/p>\n<h3>\u65e0\u7406\u6570\u7684\u51fa\u73b0<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1216s\" target=\"_blank\" rel=\"noopener\">\u5230\u4e86\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5f00\u59cb\u95ee\u81ea\u5df1<\/span><\/strong><\/a>\uff0c\\mathbb{Q}<\/span>\u4e2d\u7684\u6240\u6709\u5143\u7d20\u7684n-\u6b21\u65b9\u6839\u662f\u5426\u90fd\u6709\u660e\u786e\u5b9a\u4e49\uff1f\u4e8b\u5b9e\u4e0a\uff0c\u867d\u7136\u4e0d\u662f\u5f88\u660e\u663e\uff08\u4e0e\u51cf\u6cd5\u548c\u9664\u6cd5\u76f8\u6bd4\uff09\uff0c\u4f46\u786e\u5b9e\u5b58\u5728\u6ca1\u6709\u6709\u7406n-\u6b21\u65b9\u6839\u7684\u6709\u7406\u6570\u3002\u4e3a\u4e86\u8bf4\u660e\u8fd9\u4e00\u70b9\uff0c\u53ea\u9700\u68c0\u67e5\u4ee5\u4e0b\u793a\u4f8b\uff1a<\/p>\n\\sqrt{2}<\/span> \u4e0d\u662f\u6709\u7406\u6570\u3002<\/strong><\/em><\/p>\n\u8bc1\u660e<\/strong><\/p>\n\u6211\u4eec\u5c06\u901a\u8fc7\u53cd\u8bc1\u6cd5\u6765\u8bc1\u660e\u8fd9\u4e00\u70b9\u3002<\/p>\n\u5047\u8bbe \\sqrt{2}<\/span> \u662f\u6709\u7406\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b58\u5728p,q\\in\\mathbb{Z}<\/span>\uff0c\u5176\u4e2dq\\neq 0,<\/span> \u4f7f\u5f97 \\sqrt{2}=p\/q,<\/span> \u5e76\u4e14\u5b83\u5df2\u7ecf\u88ab\u5316\u7b80\u4e3a\u4e0d\u53ef\u7ea6\u7684\u5f62\u5f0f\u3002\u5982\u679c\u6211\u4eec\u8fd9\u6837\u505a\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4<\/p>\n2 = \\left(\\sqrt{2} \\right)^2 =\\displaystyle \\frac{p^2}{q^2} = <\/span> \\left(\\displaystyle \\frac{p}{q}\\right)^2<\/span>\n<\/span><\/p>\n\u4f46\u662f\uff0c\u8fd9\u4e0ep\/q<\/span> \u4ee5\u4e0d\u53ef\u7ea6\u5f62\u5f0f\u4e66\u5199\u7684\u4e8b\u5b9e\u76f8\u77db\u76fe\uff08\u73b0\u5728\u7ed3\u679c\u662f(p\/q)^2<\/span> \u53ef\u4ee5\u88ab\u7b80\u5316\uff0c\u5176\u7ed3\u679c\u662f2\uff09\u3002\u7531\u4e8e\u5047\u8bbe\\sqrt{2}<\/span> \u662f\u6709\u7406\u6570\u4ea7\u751f\u4e86\u77db\u76fe\uff0c\u6240\u4ee5\u5b83\u4e0d\u80fd\u662f\u6709\u7406\u6570\uff0c\u6211\u4eec\u56e0\u6b64\u8bf4\u5b83\u662f\u65e0\u7406\u6570\u3002<\/p>\n<h3>\u6269\u5c55\u5230\u5b9e\u6570<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1514s\" target=\"_blank\" rel=\"noopener\">\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0c<\/span> <\/strong><\/a>\u4e3a\u4e86\u6b63\u786e\u5b9a\u4e49n-\u6b21\u65b9\u6839\uff0c\u9700\u8981\u5c06\u6709\u7406\u6570\u6269\u5c55\u5230\u4e00\u4e2a\u65b0\u7684\u96c6\u5408\uff0c\u8fd9\u5c31\u662f\u5b9e\u6570\u96c6\uff0c\u6211\u4eec\u7528\\mathbb{R}<\/span>\u8868\u793a\uff0c\u5e76\u5305\u62ec\u6709\u7406\u6570\u548c\u65e0\u7406\u6570\u3002<\/p>\n\\mathbb{R}= \\mathbb{Q}\\cup \\mathbb{Q}^*<\/span>\n<a name=\"6\"><\/a><\/p>\n<h2>\u590d\u6570\uff1a\u5b9e\u6570\u7684\u4ee3\u6570\u95ed\u5305<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1532s\" target=\"_blank\" rel=\"noopener\">\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u5e94\u8be5\u6ce8\u610f\u4e24\u4ef6\u4e8b\uff1a<\/span><\/strong><\/a>\uff081\uff09\u5f53n<\/span> \u662f\u5076\u6570\u65f6\uff0cn-\u6b21\u65b9\u6839\u662f\u591a\u503c\u7684\uff1b\uff082\uff09\u5982\u679c\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97q\\lt 0<\/span> \u7684\\sqrt[n]{q}<\/span>\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u8fd9\u6837\u7684\u6570\u5b57\u4e0d\u80fd\u662f\u5b9e\u6570\u3002<\/p>\n\u9996\u5148\uff0c\u901a\u8fc7\u5bf9\u70b9\uff0817\uff09\u8fdb\u884c\u8f7b\u5fae\u66f4\u6539\uff0c\u5b9a\u4e49\u4e3b\u8981\u6839\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4ece\u800c\u8c08\u5230\u6839\u7684\u5b9a\u4e49\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>17*.<\/td>\n<td>q\\gt 0 \\rightarrow \\left[ 0\\lt p=\\sqrt[n]{q} \\leftrightarrow p^n=q \\right]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u7b2c\u4e8c\u4e2a\u95ee\u9898\u662f\u901a\u8fc7\u5c06\u5b9e\u6570\u6269\u5c55\u5230\u590d\u6570\u96c6\\mathbb{C}<\/span>\u6765\u89e3\u51b3\u7684\uff0c\u4f46\u8fd9\u4e2a\u6784\u9020\u5c06\u5728\u4ee5\u540e\u8ba8\u8bba\u3002<\/p>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"\u6570\u5b57\u96c6\u7684\u521d\u6b65\u4e86\u89e3 – ToposUranos.com \u6570\u5b57\u96c6\u521d\u63a2\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570 \u6458\u8981\uff1a\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u7d22\u5982\u4f55\u4f7f\u7528\u81ea\u7136\u6570\u4f5c\u4e3a\u6784\u5efa\u5176\u4ed6\u6570\u5b57\u96c6\u7684\u57fa\u7840\uff0c\u4ee5\u89e3\u51b3\u67d0\u4e9b\u64cd\u4f5c\u9650\u5236\u3002\u6211\u4eec\u5c06\u4ece\u6574\u6570\u5f00\u59cb\uff0c\u5b83\u4eec\u4f7f\u6211\u4eec\u80fd\u591f\u5e7f\u6cdb\u5730\u6267\u884c\u51cf\u6cd5\u3002\u7136\u540e\uff0c\u6211\u4eec\u5c06\u8fdb\u4e00\u6b65\u7814\u7a76\u6709\u7406\u6570\uff0c\u5b83\u4eec\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u5b8c\u6574\u7684\u9664\u6cd5\u5de5\u5177\u3002\u968f\u540e\uff0c\u6211\u4eec\u5c06\u6df1\u5165\u4e86\u89e3\u5b9e\u6570\uff0c\u4ee5\u4fbf\u80fd\u591f\u5904\u7406 n-\u6b21\u65b9\u6839\uff0c\u5e76\u63d0\u53ca\u5982\u4f55\u5f15\u5165\u590d\u6570\u4ee5\u5904\u7406\u7279\u5b9a\u573a\u666f\u4e2d\u7684 n-\u6b21\u65b9\u6839\u3002\u901a\u8fc7\u8fd9\u4e9b\u53d1\u5c55\uff0c\u5c06\u7406\u89e3\u6bcf\u4e2a\u65b0\u7684\u6570\u5b57\u96c6\u662f\u5982\u4f55\u51fa\u73b0\u7684\uff0c\u4ee5\u89e3\u51b3\u524d\u4e00\u4e2a\u96c6\u5408\u4e2d\u56fa\u6709\u7684\u95ee\u9898\u3002 \u5b66\u4e60\u76ee\u6807:\u5728\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u8bc6\u522b\u81ea\u7136\u6570\u3001\u6574\u6570\u548c\u6709\u7406\u6570\u7684\u57fa\u672c\u5c5e\u6027\u3002 \u89e3\u91ca\u5728\u4ece\u4e00\u4e2a\u6570\u5b57\u96c6\u8fc7\u6e21\u5230\u53e6\u4e00\u4e2a\u6570\u5b57\u96c6\u65f6\u7ee7\u627f\u6216\u4fee\u6539\u7684\u57fa\u672c\u5c5e\u6027\u548c\u64cd\u4f5c\u3002 \u6bd4\u8f83\u4e0d\u540c\u6570\u5b57\u96c6\u7684\u5c5e\u6027\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u3002 \u5185\u5bb9\u7d22\u5f15 \u7b80\u4ecb \u81ea\u7136\u6570\u7684\u5c5e\u6027 \u4ece\u81ea\u7136\u6570\u8fc7\u6e21\u5230\u6574\u6570 \u8dc3\u5411\u6709\u7406\u6570 \u5b9e\u6570\u548c\u65e0\u7406\u6570 \u590d\u6570\uff1a\u5b9e\u6570\u7684\u4ee3\u6570\u6761\u6b3e \u7b80\u4ecb \u5b9e\u6570\uff0c\u4ee5\u53ca\u6211\u4eec\u5728\u8fd9\u8bfe\u4e2d\u5c06\u63a2\u8ba8\u7684\u5176\u4ed6\u6570\u5b57\u96c6\uff0c\u662f\u901a\u8fc7\u6269\u5c55\u81ea\u7136\u6570\u6765\u5f15\u5165\u7684\u3002\u4e8b\u5b9e\u662f\uff0c\u5bf9\u4e8e\u4efb\u4f55\u4e24\u4e2a\u81ea\u7136\u6570\uff0c\u5e76\u4e0d\u603b\u662f\u53ef\u4ee5\u8fdb\u884c\u51cf\u6cd5\u6216\u9664\u6cd5\u8fd0\u7b97\uff0c\u800c\u8fd9\u4e9b\u6269\u5c55\u7684\u76ee\u7684\u662f\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002 \u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u81ea\u7136\u6570\u7684\u8fd0\u7b97\u548c\u5c5e\u6027\uff0c\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u5c06\u7ee7\u7eed\u6784\u5efa\u6240\u6709\u5176\u4ed6\u6570\u5b57\u96c6\uff0c\u76f4\u5230\u8fbe\u5230\u5b9e\u6570\uff0c\u5e76\u4e14\u66f4\u8fdb\u4e00\u6b65\u3002 \u81ea\u7136\u6570\u7684\u5c5e\u6027 \u5728\u5904\u7406\u81ea\u7136\u6570\u8fd0\u7b97\u65f6\uff0c\u6211\u4eec\u4e3b\u8981\u6307\u7684\u662f\u52a0\u6cd5\u548c\u4e58\u6cd5\uff0c\u4ee5\u53ca\u5b83\u4eec\u5404\u81ea\u7684\u9006\u8fd0\u7b97\u3002\u4e0b\u9762\u603b\u7ed3\u4e86\u8fd9\u4e9b\u5c5e\u6027\uff1a \u5047\u8bbe \u6211\u4eec\u9a8c\u8bc1\u4e86\uff1a 1. 2. (\u5728\u51cf\u6cd5\u7684\u60c5\u51b5\u4e0b\uff0c\u53ea\u6709\u5728\u5b9a\u4e49\u660e\u786e\u7684\u60c5\u51b5\u4e0b\u624d\u6709\u6548) 3. 4. 5. 6. 7. \u4ece\u81ea\u7136\u6570\u5230\u6574\u6570\u7684\u8fc7\u6e21 \u9996\u5148\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u6c42\u548c\u7684\u60c5\u51b5\u4e0b\uff1a \uff0c\u800c\u5bf9\u4e8e\u51cf\u6cd5\uff1a\u3002\u5f53\u4e24\u4e2a\u81ea\u7136\u6570 \u548c \u7684\u51cf\u6cd5\u6ca1\u6709\u610f\u4e49\u65f6\uff0c\u5373 \uff0c\u95ee\u9898\u51fa\u73b0\u4e86\uff1b\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u81ea\u7136\u6570\u88ab\u6269\u5c55\u5230\u6574\u6570\u96c6\uff0c\u5176\u4e2d\u8fd9\u79cd\u6027\u8d28\u7684\u51cf\u6cd5\u5f97\u5230\u4e86\u660e\u786e\u5b9a\u4e49\u3002\u6211\u4eec\u7528\u5b57\u6bcd \u8868\u793a\u8fd9\u4e2a\u65b0\u7684\u6574\u6570\u96c6\uff0c\u5b83\u5305\u62ec\u6240\u6709\u7684\u81ea\u7136\u6570\u3001\u5b83\u4eec\u7684\u52a0\u6cd5\u9006\u5143\u548c\u96f6\u3002 \u6574\u6570\u7ee7\u627f\u4e86\u6240\u6709\u81ea\u7136\u6570\u7684\u5c5e\u6027\u548c\u64cd\u4f5c\uff0c\u5e76\u5728\u7b2c\u4e8c\u4e2a\u5c5e\u6027\u4e0a\u8fdb\u884c\u4e86\u6269\u5c55\uff0c\u5f15\u5165\u4e86\u52a0\u6cd5\u9006\u5143\u548c\u52a0\u6cd5\u5355\u4f4d\u5143\u7684\u6982\u5ff5\u3002 2*. 8. 9. \u5143\u7d20 \u662f\u6211\u4eec\u6240\u8bf4\u7684 \u7684\u52a0\u6cd5\u9006\u5143\u3002 \u8df3\u5230\u6709\u7406\u6570 \u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u552f\u4e00\u6ca1\u6709\u6b63\u786e\u5b9a\u4e49\u7684\u64cd\u4f5c\u662f\u9664\u6cd5\u3002 \u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5bf9\u6574\u6570\u96c6\u8fdb\u884c\u6269\u5c55\uff0c\u5f97\u5230\u6709\u7406\u6570\u96c6\uff0c\u7531\u4ee5\u4e0b\u96c6\u5408\u7ed9\u51fa\uff1a \u8fd9\u6837\u5c31\u83b7\u5f97\u4e86\u4e00\u4e2a\u65b0\u7684\u5c5e\u6027 10. \u6bcf\u4e2a\u975e\u96f6\u7684\u6709\u7406\u6570\u90fd\u6709\u4e00\u4e2a\u4e58\u6cd5\u9006\u5143\u3002 \u7684\u4e58\u6cd5\u9006\u5143\u662f \u5bf9\u4e8e\u8fd9\u4e9b\u6570\u5b57\u3001\u64cd\u4f5c\u548c\u5c5e\u6027\uff0c\u5b9a\u4e49\u4e86\u65b0\u7684\u64cd\u4f5c\u53ca\u5176\u5c5e\u6027\u3002\u5728\u8fd9\u91cc\uff0c\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5b9a\u4e49\u6709\u7406\u6570 […]<\/p>\n","protected":false},"author":1,"featured_media":25034,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":16,"footnotes":""},"categories":[1035,591,575],"tags":[],"class_list":["post-24926","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1035","category-591","category-575"],"yoast_head":"\n<title>\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\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\/\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\" \/>\n<meta property=\"og:description\" content=\"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/zh\/\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\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=\"2021-03-16T00:00:44+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-03-02T19:54:14+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/naturales-captura-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\" \/>\n<meta name=\"twitter:description\" content=\"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/naturales-captura.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\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\",\"datePublished\":\"2021-03-16T00:00:44+00:00\",\"dateModified\":\"2025-03-02T19:54:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/\"},\"wordCount\":554,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/conjuntosnumericos-3.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\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/\",\"name\":\"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/conjuntosnumericos-3.jpg\",\"datePublished\":\"2021-03-16T00:00:44+00:00\",\"dateModified\":\"2025-03-02T19:54:14+00:00\",\"description\":\"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/conjuntosnumericos-3.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/conjuntosnumericos-3.jpg\",\"width\":1081,\"height\":399,\"caption\":\"\u6570\u503c\u96c6\u5408\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/zh\\\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%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\":\"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\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_head_json":{"title":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570 - toposuranos.com\/material","description":"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\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\/\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\/","og_locale":"es_ES","og_type":"article","og_title":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570","og_description":"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002","og_url":"https:\/\/toposuranos.com\/material\/zh\/\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-16T00:00:44+00:00","article_modified_time":"2025-03-02T19:54:14+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/naturales-captura-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570","twitter_description":"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/naturales-captura.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\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570","datePublished":"2021-03-16T00:00:44+00:00","dateModified":"2025-03-02T19:54:14+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/"},"wordCount":554,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/conjuntosnumericos-3.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\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/","url":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/","name":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/conjuntosnumericos-3.jpg","datePublished":"2021-03-16T00:00:44+00:00","dateModified":"2025-03-02T19:54:14+00:00","description":"\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570\uff0c\u521d\u6b65\u4e86\u89e3\u6570\u5b57\u96c6\u5408\u7684\u6784\u9020\u3002","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/conjuntosnumericos-3.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/conjuntosnumericos-3.jpg","width":1081,"height":399,"caption":"\u6570\u503c\u96c6\u5408"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%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":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\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\/24926","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=24926"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/24926\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/25034"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=24926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=24926"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=24926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":24926,"date":"2021-03-16T00:00:44","date_gmt":"2021-03-16T00:00:44","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=24926"},"modified":"2025-03-02T19:54:14","modified_gmt":"2025-03-02T19:54:14","slug":"%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%95%b0%e5%80%bc%e9%9b%86%e5%90%88%ef%bc%9a%e4%bb%8e%e8%87%aa%e7%84%b6%e6%95%b0%e5%88%b0%e5%a4%8d%e6%95%b0\/","title":{"rendered":"\u6570\u503c\u96c6\u5408\uff1a\u4ece\u81ea\u7136\u6570\u5230\u590d\u6570"},"content":{"rendered":"