\u6570\u96c6\u5408\u3078\u306e\u7b2c\u4e00\u306e\u30a2\u30d7\u30ed\u30fc\u30c1 – ToposUranos.com<\/title> <\/head> <body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6570\u96c6\u5408\u3078\u306e\u7b2c\u4e00\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\uff1a\u81ea\u7136\u6570\u304b\u3089\u8907\u7d20\u6570\u307e\u3067<\/h1>\n<\/center><\/p>\n\u6982\u8981:<\/strong><\/br>\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u81ea\u7136\u6570\u304c\u4ed6\u306e\u6570\u306e\u96c6\u5408\u3092\u69cb\u6210\u3059\u308b\u57fa\u790e\u3068\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u5229\u7528\u3067\u304d\u308b\u304b\u3092\u63a2\u308a\u3001\u7279\u5b9a\u306e\u6f14\u7b97\u4e0a\u306e\u5236\u9650\u3092\u514b\u670d\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u6e1b\u7b97\u3092\u5e83\u304f\u884c\u3048\u308b\u3088\u3046\u306b\u3057\u3066\u304f\u308c\u308b\u6574\u6570\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u6b21\u306b\u3001\u5b8c\u5168\u306a\u5272\u308a\u7b97\u3092\u53ef\u80fd\u306b\u3059\u308b\u6709\u7406\u6570\u3078\u9032\u307f\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001n \u6b21\u6839\u3092\u6271\u3046\u305f\u3081\u306b\u5b9f\u6570\u3078\u3068\u9032\u307f\u3001\u8907\u7d20\u6570\u304c n \u6b21\u6839\u306e\u7279\u5b9a\u306e\u72b6\u6cc1\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306b\u3069\u306e\u3088\u3046\u306b\u5c0e\u5165\u3055\u308c\u308b\u304b\u3092\u8ff0\u3079\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5c55\u958b\u3092\u901a\u3058\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u65b0\u3057\u3044\u6570\u306e\u96c6\u5408\u304c\u524d\u306e\u96c6\u5408\u306b\u56fa\u6709\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3069\u306e\u3088\u3046\u306b\u751f\u3058\u308b\u304b\u304c\u7406\u89e3\u3055\u308c\u307e\u3059\u3002<\/em><\/p>\n\u5b66\u7fd2\u76ee\u6a19<\/u>:<\/strong> \u3053\u306e\u6388\u696d\u3092\u7d42\u3048\u308b\u3068\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059:<\/p>\n<ol>\n<li>\u8b58\u5225\u3059\u308b<\/strong> \u81ea\u7136\u6570\u3001\u6574\u6570\u3001\u6709\u7406\u6570\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3002<\/li>\n<li>\u89e3\u91c8\u3059\u308b<\/strong> \u3042\u308b\u6570\u306e\u96c6\u5408\u304b\u3089\u5225\u306e\u96c6\u5408\u3078\u79fb\u884c\u3059\u308b\u969b\u306b\u53d7\u3051\u7d99\u304c\u308c\u308b\u3001\u307e\u305f\u306f\u5909\u66f4\u3055\u308c\u308b\u57fa\u672c\u7684\u306a\u6027\u8cea\u3068\u6f14\u7b97\u3002<\/li>\n<li>\u6bd4\u8f03\u3059\u308b<\/strong> \u3055\u307e\u3056\u307e\u306a\u6570\u306e\u96c6\u5408\u306e\u6027\u8cea\u3068\u305d\u308c\u3089\u304c\u3069\u306e\u3088\u3046\u306b\u95a2\u9023\u3057\u3066\u3044\u308b\u304b\u3002<\/li>\n<\/ol>\n\u5185\u5bb9\u76ee\u6b21<\/u><\/strong> \n<a href=\"#1\">\u5c0e\u5165<\/a> \n<a href=\"#2\">\u81ea\u7136\u6570\u306e\u6027\u8cea<\/a> \n<a href=\"#3\">\u81ea\u7136\u6570\u304b\u3089\u6574\u6570\u3078\u306e\u79fb\u884c<\/a> \n<a href=\"#4\">\u6709\u7406\u6570\u3078\u306e\u98db\u8e8d<\/a> \n<a href=\"#5\">\u5b9f\u6570\u3068\u7121\u7406\u6570<\/a> \n<a href=\"#6\">\u8907\u7d20\u6570\uff1a\u5b9f\u6570\u306e\u4ee3\u6570\u7684\u9589\u5305<\/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>\u5c0e\u5165<\/h2>\n<div class=\"content\">\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=96s\" target=\"_blank\" rel=\"noopener\">\u5b9f\u6570\u306f\u3001\u672c\u8b1b\u7fa9\u3067\u63a2\u7a76\u3059\u308b\u4ed6\u306e\u6570\u306e\u96c6\u5408\u3068\u3068\u3082\u306b\u3001<\/strong><\/span><\/a>\u81ea\u7136\u6570\u306e\u62e1\u5f35\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u307e\u3059\u3002\u4efb\u610f\u306e\u4e8c\u3064\u306e\u81ea\u7136\u6570\u3067\u306f\u3001\u6e1b\u7b97\u3084\u5272\u308a\u7b97\u3092\u5e38\u306b\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u306f\u9650\u3089\u305a\u3001\u3053\u308c\u3089\u306e\u62e1\u5f35\u306f\u305d\u306e\u4e0d\u90fd\u5408\u3092\u89e3\u6d88\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\u672c\u8b1b\u7fa9\u306e\u9593\u306b\u3001<a href=\"https:\/\/toposuranos.com\/operaciones-con-numeros-naturales\/\" rel=\"noopener\" target=\"_blank\">\u81ea\u7136\u6570\u306e\u6f14\u7b97\u3068\u6027\u8cea<\/strong><\/a>\u3092\u5fa9\u7fd2\u3057\u3001\u305d\u306e\u57fa\u76e4\u306e\u4e0a\u306b\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u6570\u306e\u96c6\u5408\u306e\u69cb\u7bc9\u3078\u9032\u307f\u3001\u5b9f\u6570\u306b\u5230\u9054\u3057\u3055\u3089\u306b\u306f\u305d\u306e\u5148\u307e\u3067\u9032\u307f\u307e\u3059\u3002<\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>\u81ea\u7136\u6570\u306e\u6027\u8cea<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=214s\" target=\"_blank\" rel=\"noopener\">\u81ea\u7136\u6570\u306b\u5bfe\u3059\u308b\u6f14\u7b97\u3092\u6271\u3046\u3068\u304d\u3001<\/span><\/strong><\/a>\u4e3b\u306b\u52a0\u6cd5\u3068\u4e57\u6cd5\u304a\u3088\u3073\u305d\u308c\u305e\u308c\u306e\u9006\u6f14\u7b97\u3092\u6307\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3053\u308c\u3089\u306e\u6027\u8cea\u3092\u307e\u3068\u3081\u307e\u3059:<\/p>\na,b,c\\in\\mathbb{N}<\/span> \u3067\u3042\u308b\u3068\u3059\u308b\u3068\u3001\u6b21\u306e\u3053\u3068\u304c\u6210\u308a\u7acb\u3061\u307e\u3059:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>1. <\/td>\n<td>a + b = b + a<\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left;\">\n<td>2. <\/td>\n<td>a \\pm (b \\pm c) = (a\\pm b)\\pm c <\/span> (en el caso de la resta, es v\u00e1lida siempre que est\u00e9 bien definida)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left;\">\n<td>3. <\/td>\n<td>a\\cdot b = b \\cdot a <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left;\">\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;\">\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;\">\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;\">\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>\u81ea\u7136\u6570\u304b\u3089\u6574\u6570\u3078\u306e\u79fb\u884c<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=418s\" target=\"_blank\" rel=\"noopener\">\u6700\u521d\u306b\u6ce8\u610f\u3059\u3079\u304d\u70b9\u306f\u3001\u52a0\u7b97\u306e\u5834\u5408\u306b\u306f\u6b21\u306e\u3053\u3068\u3067\u3059:<\/span><\/strong><\/a> (\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N})<\/span>\u3001\u4e00\u65b9\u3001\u6e1b\u7b97\u3067\u306f: (\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N} \\leftrightarrow a\\gt b)<\/span>\u3002\u81ea\u7136\u6570 a<\/span> \u3068 b<\/span> \u306e\u6e1b\u7b97\u304c a\\leq b<\/span> \u306e\u5834\u5408\u306b\u610f\u5473\u3092\u6301\u305f\u306a\u3044\u3068\u3044\u3046\u4e0d\u90fd\u5408\u304c\u751f\u3058\u307e\u3059\u3002\u3053\u306e\u72b6\u6cc1\u3092\u4fee\u6b63\u3059\u308b\u305f\u3081\u306b\u3001\u81ea\u7136\u6570\u3092\u6574\u6570\u306e\u96c6\u5408\u3078\u3068\u62e1\u5f35\u3057\u3001\u305d\u306e\u3088\u3046\u306a\u6e1b\u7b97\u306b\u660e\u78ba\u306a\u5024\u3092\u4e0e\u3048\u307e\u3059\u3002\u3053\u306e\u65b0\u3057\u3044\u6574\u6570<\/strong>\u306e\u96c6\u5408\u3092 \\mathbb{Z}<\/span> \u3068\u3044\u3046\u6587\u5b57\u3067\u8868\u3057\u3001\u305d\u308c\u306f\u3059\u3079\u3066\u306e\u81ea\u7136\u6570\u3001\u305d\u308c\u3089\u306e\u52a0\u6cd5\u9006\u5143\u304a\u3088\u3073\u30bc\u30ed\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\u3002<\/p>\n\\mathbb{Z} = \\{\\cdots, -3,-2,-1,0,1,2,3,\\cdots \\}<\/span>\n\u6574\u6570\u306f\u81ea\u7136\u6570\u306e\u3059\u3079\u3066\u306e\u6027\u8cea\u3068\u6f14\u7b97\u3092\u7d99\u627f\u3057\u3001\u7b2c\u4e8c\u306e\u6027\u8cea\u304c\u62e1\u5f35\u3055\u308c\u3001\u52a0\u6cd5\u9006\u5143\u3068\u52a0\u6cd5\u5358\u4f4d\u5143\u306e\u6982\u5ff5\u304c\u5c0e\u5165\u3055\u308c\u307e\u3059\u3002<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: left;\">\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;\">\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;\">\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>\nb=-a<\/span> \u3068\u3044\u3046\u8981\u7d20\u3092 a<\/span> \u306e\u52a0\u6cd5\u9006\u5143<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>\u6709\u7406\u6570\u3078\u306e\u98db\u8e8d<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=755s\" target=\"_blank\" rel=\"noopener\">\u3053\u306e\u6642\u70b9\u3067\u3001\u307e\u3060\u6b63\u3057\u304f\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u552f\u4e00\u306e\u6f14\u7b97\u306f\u5272\u308a\u7b97\u3067\u3059\u3002<\/span><\/strong><\/a> \u3053\u308c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u6574\u6570\u306e\u96c6\u5408\u3092\u6b21\u306e\u96c6\u5408\u3067\u4e0e\u3048\u3089\u308c\u308b\u6709\u7406\u6570\u306e\u96c6\u5408\u3078\u3068\u62e1\u5f35\u3057\u307e\u3059\u3002<\/p>\n\\mathbb{Q}=\\left\\{a= \\displaystyle\\frac{n}{m}\\;|\\;n,m\\in\\mathbb{Z}\\wedge m\\neq 0 \\right\\}<\/span>\n\u3053\u308c\u306b\u3088\u308a\u65b0\u3057\u3044\u6027\u8cea\u304c\u5f97\u3089\u308c\u307e\u3059<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\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;\">\n<td colspan=\"2\">\u96f6\u3067\u306a\u3044\u3059\u3079\u3066\u306e\u6709\u7406\u6570\u306b\u306f\u4e57\u6cd5\u9006\u5143\u304c\u5b58\u5728\u3057\u307e\u3059\u3002 a<\/span> \u306e\u4e57\u6cd5\u9006\u5143\u306f a^{-1}<\/span> \u3067\u3059\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u3053\u308c\u3089\u306e\u6570\u3001\u6f14\u7b97\u304a\u3088\u3073\u6027\u8cea\u306b\u3088\u308a\u3001\u65b0\u3057\u3044\u6f14\u7b97\u304c\u305d\u306e\u6027\u8cea\u3068\u3068\u3082\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u6709\u7406\u6570 q<\/span> \u306e n \u4e57\u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059<\/p>\nq^n = \\underbrace{q\\cdot q \\cdot \\cdots \\cdot q}_{n\\;veces};<\/span> \u305f\u3060\u3057 n\\in\\mathbb{N}<\/span>\nq^{-n}= \\displaystyle \\frac{1}{q^n}<\/span>\n\u3053\u308c\u304b\u3089\u3001 q\\neq 0<\/span> \u306e\u3068\u304d\u5e38\u306b\u6b21\u306e\u3088\u3046\u306b\u8a00\u3048\u307e\u3059<\/p>\nq^0 = 1<\/span>\n\u3055\u3089\u306b\u30010 \u3067\u5272\u308b\u3053\u3068\u304c\u306a\u3044\u9650\u308a\u3001\u4efb\u610f\u306e\u6709\u7406\u6570 a,b<\/span> \u3068\u6574\u6570 n,m<\/span> \u306b\u3064\u3044\u3066\u3001\u6b21\u306e\u6027\u8cea\u304c\u6210\u308a\u7acb\u3061\u307e\u3059:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\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;\">\n<td>12.<\/td>\n<td>(a^n)^m = a^{n\\cdot m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify;\">\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;\">\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;\">\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>\u5b9f\u6570\u3068\u7121\u7406\u6570<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1031s\" target=\"_blank\" rel=\"noopener\">\u52a0\u7b97\u306e\u9006\u6f14\u7b97\u3067\u3042\u308b\u6e1b\u7b97\u3068\u3001\u7a4d\u306e\u9006\u6f14\u7b97\u3067\u3042\u308b\u9664\u6cd5\u304c<\/span><\/strong><\/a>\u305d\u308c\u305e\u308c\u81ea\u7136\u6570\u3092\u6574\u6570\u304a\u3088\u3073\u6709\u7406\u6570\u3078\u3068\u62e1\u5f35\u3057\u3066\u6f14\u7b97\u3092\u3088\u304f\u5b9a\u7fa9\u3059\u308b\u5fc5\u8981\u3092\u751f\u3058\u3055\u305b\u305f\u3088\u3046\u306b\u3001\u7d2f\u4e57\u3067\u3082\u540c\u69d8\u306e\u3053\u3068\u304c\u8d77\u3053\u308a\u307e\u3059\u3002 n<\/span> \u4e57\u306e\u9006\u6f14\u7b97\u306f n<\/span> \u4e57\u6839\u3067\u3059\u3002<\/p>\n<h3>\u6839\u306e\u5b9a\u7fa9<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1071s\" target=\"_blank\" rel=\"noopener\">n<\/span> \u3092 1 \u3088\u308a\u5927\u304d\u3044\u6574\u6570\u3068\u3057<\/span><\/strong><\/a> p,q<\/span> \u3092\u4efb\u610f\u306e\u6709\u7406\u6570\u3068\u3059\u308b\u3068\u3001 q<\/span> \u306e n<\/span> \u4e57\u6839\u306f\u6b21\u306e\u898f\u5247\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>16.<\/td>\n<td>q=0 \\rightarrow \\sqrt[n]{q} = 0<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify;\">\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;\">\n<td>18.<\/td>\n<td> \\left[ q \\lt 0 \\wedge n {\\;es\\;impar} \\right]\\rightarrow \\left[ \\sqrt[n]{q} = p \\leftrightarrow p^n = q \\right]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u8981\u7d04\u3059\u308b\u3068\u3001 q<\/span> \u306e n<\/span> \u4e57\u6839\u3068\u306f\u3001 n<\/span> \u4e57\u3057\u305f\u3068\u304d\u306b q<\/span> \u3092\u8fd4\u3059\u6570 p<\/span> \u306e\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u5834\u5408\u3001 n=2<\/span> \u306e\u3068\u304d\u306f\u3001 \\sqrt[2]{q}<\/span> \u3068\u66f8\u304f\u4ee3\u308f\u308a\u306b\u7c21\u5358\u306b \\sqrt{q}<\/span> \u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<h3>\u7121\u7406\u6570\u306e\u51fa\u73fe<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1216s\" target=\"_blank\" rel=\"noopener\">\u3053\u3053\u307e\u3067\u6765\u308b\u3068\u79c1\u305f\u3061\u306f\u6b21\u306e\u3088\u3046\u306b\u554f\u3044\u304b\u3051\u307e\u3059<\/span><\/strong><\/a> \\mathbb{Q}<\/span> \u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u306b\u3064\u3044\u3066 n<\/span> \u4e57\u6839\u306f\u3046\u307e\u304f\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u6e1b\u7b97\u3084\u9664\u7b97\u306e\u5834\u5408\u3068\u6bd4\u3079\u308b\u3068\u305d\u308c\u307b\u3069\u81ea\u660e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001 n<\/span> \u4e57\u6839\u304c\u6709\u7406\u6570\u306b\u306a\u3089\u306a\u3044\u6709\u7406\u6570\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u78ba\u8a8d\u3059\u308b\u306b\u306f\u6b21\u306e\u4f8b\u3092\u898b\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>\n\\sqrt{2}<\/span> \u306f\u6709\u7406\u6570\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/strong><\/em><\/p>\n\u8a3c\u660e<\/strong><\/p>\n\u3053\u308c\u3092\u80cc\u7406\u6cd5\u306b\u3088\u3063\u3066\u793a\u3057\u307e\u3059\u3002<\/p>\n\\sqrt{2}<\/span> \u304c\u6709\u7406\u6570\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3064\u307e\u308a p,q\\in\\mathbb{Z}<\/span> \u3067 q\\neq 0<\/span> \u306e\u3082\u306e\u304c\u5b58\u5728\u3057\u3001 \\sqrt{2}=p\/q<\/span> \u3068\u306a\u308a\u3001\u3055\u3089\u306b\u3053\u306e\u5206\u6570\u306f\u65e2\u7d04\u306a\u5f62\u307e\u3067\u7d04\u5206\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u8a00\u3048\u307e\u3059\u3002<\/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\u3057\u304b\u3057\u3001\u3053\u308c\u306f p\/q<\/span> \u304c\u65e2\u7d04\u5206\u6570\u3067\u3042\u3063\u305f\u3068\u3044\u3046\u4e8b\u5b9f\u3068\u77db\u76fe\u3057\u307e\u3059\uff08\u4eca\u3084 (p\/q)^2<\/span> \u3092\u7d04\u5206\u3067\u304d\u3001\u305d\u306e\u7d50\u679c\u304c 2 \u306b\u306a\u308b\uff09\u3002\u3057\u305f\u304c\u3063\u3066 \\sqrt{2}<\/span> \u304c\u6709\u7406\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u4eee\u5b9a\u306f\u77db\u76fe\u3092\u751f\u307f\u3001\u3053\u306e\u6570\u306f\u6709\u7406\u6570\u3067\u306f\u3042\u308a\u5f97\u305a\u3001\u3057\u305f\u304c\u3063\u3066\u7121\u7406\u6570\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002<\/p>\n<h3>\u5b9f\u6570\u3078\u306e\u62e1\u5f35<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1514s\" target=\"_blank\" rel=\"noopener\">\u3053\u308c\u3089\u306e\u7d50\u679c\u306f\u6b21\u306e\u4e8b\u5b9f\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002<\/span> <\/strong><\/a>n<\/span> \u4e57\u6839\u3092\u6b63\u3057\u304f\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u6709\u7406\u6570\u3092\u65b0\u3057\u3044\u96c6\u5408\u306b\u62e1\u5f35\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u304c \\mathbb{R}<\/span> \u3067\u8868\u3055\u308c\u308b\u5b9f\u6570\u306e\u96c6\u5408\u3067\u3001\u3053\u308c\u306f\u6709\u7406\u6570\u3068\u7121\u7406\u6570\u306e\u4e21\u65b9\u3092\u542b\u307f\u307e\u3059\u3002<\/p>\n\\mathbb{R}= \\mathbb{Q}\\cup \\mathbb{Q}^*<\/span>\n<a name=\"6\"><\/a><\/p>\n<h2>\u8907\u7d20\u6570\uff1a\u5b9f\u6570\u306e\u4ee3\u6570\u7684\u9589\u5305<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1532s\" target=\"_blank\" rel=\"noopener\">\u3053\u306e\u6642\u70b9\u3067\u79c1\u305f\u3061\u306f\u4e8c\u3064\u306e\u3053\u3068\u306b\u6ce8\u610f\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\uff1a<\/span><\/strong><\/a> (1) n<\/span> \u304c\u5076\u6570\u306e\u5834\u5408\u3001 n<\/span> \u4e57\u6839\u306f\u591a\u5024\u3068\u306a\u308a\u3001 (2) \u3055\u3089\u306b q\\lt 0<\/span> \u3067 \\sqrt[n]{q}<\/span> \u3092\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u3001\u305d\u306e\u3088\u3046\u306a\u6570\u306f\u5b9f\u6570\u3067\u306f\u3042\u308a\u5f97\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\u7b2c\u4e00\u306e\u70b9\u306f\u3001\u6839\u306e\u5b9a\u7fa9\u306b\u95a2\u3059\u308b\u9805\u76ee (17) \u306b\u8efd\u5fae\u306a\u5909\u66f4\u3092\u52a0\u3048\u3001\u4e3b\u6839<\/strong> \u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u89e3\u6c7a\u3057\u307e\u3059\u3002\u305d\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\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\u306e\u70b9\u306f\u3001\u5b9f\u6570\u306e\u96c6\u5408\u3092\u8907\u7d20\u6570 \\mathbb{C}<\/span> \u306e\u96c6\u5408\u3078\u3068\u62e1\u5f35\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u9054\u6210\u3055\u308c\u307e\u3059\u304c\u3001\u3053\u306e\u69cb\u6210\u306b\u3064\u3044\u3066\u306f\u5f8c\u307b\u3069\u6271\u3044\u307e\u3059\u3002<\/p>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"\u6570\u96c6\u5408\u3078\u306e\u7b2c\u4e00\u306e\u30a2\u30d7\u30ed\u30fc\u30c1 – ToposUranos.com \u6570\u96c6\u5408\u3078\u306e\u7b2c\u4e00\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\uff1a\u81ea\u7136\u6570\u304b\u3089\u8907\u7d20\u6570\u307e\u3067 \u6982\u8981:\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u81ea\u7136\u6570\u304c\u4ed6\u306e\u6570\u306e\u96c6\u5408\u3092\u69cb\u6210\u3059\u308b\u57fa\u790e\u3068\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u5229\u7528\u3067\u304d\u308b\u304b\u3092\u63a2\u308a\u3001\u7279\u5b9a\u306e\u6f14\u7b97\u4e0a\u306e\u5236\u9650\u3092\u514b\u670d\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u6e1b\u7b97\u3092\u5e83\u304f\u884c\u3048\u308b\u3088\u3046\u306b\u3057\u3066\u304f\u308c\u308b\u6574\u6570\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u6b21\u306b\u3001\u5b8c\u5168\u306a\u5272\u308a\u7b97\u3092\u53ef\u80fd\u306b\u3059\u308b\u6709\u7406\u6570\u3078\u9032\u307f\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001n \u6b21\u6839\u3092\u6271\u3046\u305f\u3081\u306b\u5b9f\u6570\u3078\u3068\u9032\u307f\u3001\u8907\u7d20\u6570\u304c n \u6b21\u6839\u306e\u7279\u5b9a\u306e\u72b6\u6cc1\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306b\u3069\u306e\u3088\u3046\u306b\u5c0e\u5165\u3055\u308c\u308b\u304b\u3092\u8ff0\u3079\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5c55\u958b\u3092\u901a\u3058\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u65b0\u3057\u3044\u6570\u306e\u96c6\u5408\u304c\u524d\u306e\u96c6\u5408\u306b\u56fa\u6709\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3069\u306e\u3088\u3046\u306b\u751f\u3058\u308b\u304b\u304c\u7406\u89e3\u3055\u308c\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19:\u3053\u306e\u6388\u696d\u3092\u7d42\u3048\u308b\u3068\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059: \u8b58\u5225\u3059\u308b \u81ea\u7136\u6570\u3001\u6574\u6570\u3001\u6709\u7406\u6570\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3002 \u89e3\u91c8\u3059\u308b \u3042\u308b\u6570\u306e\u96c6\u5408\u304b\u3089\u5225\u306e\u96c6\u5408\u3078\u79fb\u884c\u3059\u308b\u969b\u306b\u53d7\u3051\u7d99\u304c\u308c\u308b\u3001\u307e\u305f\u306f\u5909\u66f4\u3055\u308c\u308b\u57fa\u672c\u7684\u306a\u6027\u8cea\u3068\u6f14\u7b97\u3002 \u6bd4\u8f03\u3059\u308b \u3055\u307e\u3056\u307e\u306a\u6570\u306e\u96c6\u5408\u306e\u6027\u8cea\u3068\u305d\u308c\u3089\u304c\u3069\u306e\u3088\u3046\u306b\u95a2\u9023\u3057\u3066\u3044\u308b\u304b\u3002 \u5185\u5bb9\u76ee\u6b21 \u5c0e\u5165 \u81ea\u7136\u6570\u306e\u6027\u8cea \u81ea\u7136\u6570\u304b\u3089\u6574\u6570\u3078\u306e\u79fb\u884c \u6709\u7406\u6570\u3078\u306e\u98db\u8e8d \u5b9f\u6570\u3068\u7121\u7406\u6570 \u8907\u7d20\u6570\uff1a\u5b9f\u6570\u306e\u4ee3\u6570\u7684\u9589\u5305 \u5c0e\u5165 \u5b9f\u6570\u306f\u3001\u672c\u8b1b\u7fa9\u3067\u63a2\u7a76\u3059\u308b\u4ed6\u306e\u6570\u306e\u96c6\u5408\u3068\u3068\u3082\u306b\u3001\u81ea\u7136\u6570\u306e\u62e1\u5f35\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u307e\u3059\u3002\u4efb\u610f\u306e\u4e8c\u3064\u306e\u81ea\u7136\u6570\u3067\u306f\u3001\u6e1b\u7b97\u3084\u5272\u308a\u7b97\u3092\u5e38\u306b\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u306f\u9650\u3089\u305a\u3001\u3053\u308c\u3089\u306e\u62e1\u5f35\u306f\u305d\u306e\u4e0d\u90fd\u5408\u3092\u89e3\u6d88\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002 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