{"id":35295,"date":"2024-12-20T13:00:52","date_gmt":"2024-12-20T13:00:52","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35295"},"modified":"2025-12-11T17:09:11","modified_gmt":"2025-12-11T17:09:11","slug":"weierstrass-%e3%81%ae%e6%a5%b5%e5%80%a4%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/weierstrass-%e3%81%ae%e6%a5%b5%e5%80%a4%e5%ae%9a%e7%90%86\/","title":{"rendered":"Weierstrass \u306e\u6975\u5024\u5b9a\u7406"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>Weierstrass \u306e\u6975\u5024\u5b9a\u7406<\/h1>\n<p style=\"text-align:center;\"><em>\u306a\u305c\u591a\u304f\u306e\u6700\u9069\u5316\u554f\u984c\u306b\u304a\u3044\u3066\u3001\u300c\u6700\u5927\u5024\u306f\u5b58\u5728\u3059\u308b\u300d\u3042\u308b\u3044\u306f\u300c\u5fc5\u305a\u6700\u5c0f\u5024\u304c\u3042\u308b\u300d\u3068\u307b\u3068\u3093\u3069\u5f53\u7136\u306e\u3088\u3046\u306b\u524d\u63d0\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5b9f\u969b\u306b\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u7d50\u8ad6\u3092\u5fc5\u305a\u3057\u3082\u4fdd\u8a3c\u3059\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<strong>Weierstrass \u306e\u5b9a\u7406<\/strong>\u3053\u305d\u304c\u3053\u306e\u7591\u554f\u3092\u89e3\u6c7a\u3059\u308b\u6b20\u3051\u3066\u3044\u305f\u8981\u7d20\u3067\u3042\u308a\u3001\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u9023\u7d9a\u95a2\u6570\u304c\u6709\u754c\u3067\u3042\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u6975\u5024\u3092\u5b9f\u969b\u306b\u9054\u6210\u3059\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u672c\u7a3f\u3067\u306f\u3001\u5b9a\u7406\u306e\u6b63\u78ba\u306a\u8a18\u8ff0\u3092\u78ba\u8a8d\u3057\u3001\u70b9\u3054\u3068\u306e\u9023\u7d9a\u6027\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u3001\u4e0a\u9650\u516c\u7406\u306b\u57fa\u3065\u304f\u53b3\u5bc6\u306a\u8a3c\u660e\u3092\u4e01\u5be7\u306b\u69cb\u7bc9\u3057\u3001\u3055\u3089\u306b\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u4e0a\u306e\u9023\u7d9a\u95a2\u6570\u3068\u3044\u3046\u73fe\u4ee3\u7684\u67a0\u7d44\u307f\u306b\u3088\u308b\u89e3\u91c8\u306b\u3064\u3044\u3066\u3082\u8ad6\u3058\u307e\u3059\u3002\u8aad\u307f\u7d42\u3048\u308b\u9803\u306b\u306f\u3001\u5358\u306b\u5b9a\u7406\u3092\u6697\u8a18\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u306a\u305c\u305d\u308c\u304c\u6210\u308a\u7acb\u3064\u306e\u304b\u3001\u305d\u3057\u3066\u306a\u305c\u89e3\u6790\u5b66\u3001\u6700\u9069\u5316\u3001\u5fdc\u7528\u30e2\u30c7\u30eb\u306b\u304a\u3044\u3066\u7e70\u308a\u8fd4\u3057\u73fe\u308c\u308b\u306e\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><b>\u5b66\u7fd2\u76ee\u6a19<\/b><\/p>\n<ol>\n<li>\n    <strong>Weierstrass \u306e\u5b9a\u7406\u306e\u5185\u5bb9\u3092\u7406\u89e3\u3059\u308b\u3002<\/strong><br \/>\n    \u5b9a\u7406\u306e\u524d\u63d0\uff08\u9023\u7d9a\u95a2\u6570\u304c\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3053\u3068\uff09\u3068\u4e3b\u8981\u7d50\u8ad6\u3067\u3042\u308b\u6709\u754c\u6027\u304a\u3088\u3073\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u306e\u5b58\u5728\u3092\u6b63\u78ba\u306b\u628a\u63e1\u3059\u308b\u3002\n  <\/li>\n<li>\n    <strong>\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u306e\u89b3\u70b9\u304b\u3089 Weierstrass \u306e\u5b9a\u7406\u3092\u89e3\u91c8\u3059\u308b\u3002<\/strong><br \/>\n    \u9023\u7d9a\u95a2\u6570\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3092\u6975\u5024\u304c\u9054\u6210\u3055\u308c\u308b\u96c6\u5408\u3078\u5199\u3059\u3068\u3044\u3046\u73fe\u4ee3\u7684\u8868\u73fe\u3092\u7528\u3044\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u306e\u5834\u5408\u3092\u5b9f\u89e3\u6790\u306b\u304a\u3051\u308b\u4e00\u822c\u7684\u67a0\u7d44\u307f\u3068\u7d50\u3073\u4ed8\u3051\u3066\u8ff0\u3079\u308b\u3002\n  <\/li>\n<li>\n    <strong>Weierstrass \u306e\u5b9a\u7406\u3068\u6700\u9069\u5316\u554f\u984c\u306e\u95a2\u4fc2\u3092\u7406\u89e3\u3059\u308b\u3002<\/strong><br \/>\n    \u591a\u304f\u306e\u4e00\u5909\u6570\u6700\u9069\u5316\u554f\u984c\u306b\u304a\u3044\u3066\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u306e\u5b58\u5728\u3092\u4fdd\u8a3c\u3059\u308b\u7406\u8ad6\u7684\u57fa\u76e4\u3068\u3057\u3066\u3001\u3053\u306e\u5b9a\u7406\u304c\u679c\u305f\u3059\u5f79\u5272\u3092\u628a\u63e1\u3059\u308b\uff08\u7406\u8ad6\u7684\u72b6\u6cc1\u30fb\u5fdc\u7528\u72b6\u6cc1\u306e\u53cc\u65b9\u3092\u542b\u3080\uff09\u3002\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u76ee\u6b21<\/u>:<\/b><br \/>\n<a href=\"#1\"><b>\u5e8f\u8ad6<\/b><\/a><br \/>\n<a href=\"#2\"><b>Weierstrass \u306e\u5b9a\u7406\u306e\u8a18\u8ff0<\/b><\/a><br \/>\n<a href=\"#3\">\u8a3c\u660e<\/a><br \/>\n<a href=\"#4\">\u30b9\u30c6\u30c3\u30d7 1\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306b\u304a\u3051\u308b\u70b9\u3054\u3068\u306e\u9023\u7d9a\u6027<\/a><br \/>\n<a href=\"#5\">\u30b9\u30c6\u30c3\u30d7 2\uff1a\u9023\u7d9a\u6027\u306b\u5bfe\u5fdc\u3059\u308b\u958b\u88ab\u8986<\/a><br \/>\n<a href=\"#6\">\u30b9\u30c6\u30c3\u30d7 3\uff1a<span dir=\"ltr\">[a,b]<\/span> \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u3068\u6709\u9650\u90e8\u5206\u88ab\u8986<\/a><br \/>\n<a href=\"#7\">\u30b9\u30c6\u30c3\u30d7 4\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u4f9d\u5b58\u3057\u306a\u3044 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u306e\u69cb\u6210\uff08\u5747\u7b49\u9023\u7d9a\u6027\uff09<\/a><br \/>\n<a href=\"#8\">\u30b9\u30c6\u30c3\u30d7 5\uff1a\u5747\u7b49\u9023\u7d9a\u6027\u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306b\u304a\u3051\u308b <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u306e\u6709\u754c\u6027\u3078<\/a><br \/>\n<a href=\"#9\">\u30b9\u30c6\u30c3\u30d7 6\uff1a\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306e\u5b58\u5728<\/a><br \/>\n<a href=\"#10\"><b>\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u306b\u3088\u308b\u89e3\u91c8\u3068\u7d50\u8ad6<\/b><\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/N5mSrhJgCds\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/br><\/p>\n<h2>\u5e8f\u8ad6<\/h2>\n<p>\n<strong>Weierstrass \u306e\u6975\u5024\u5b9a\u7406<\/strong>\u306f\u3001\u5b9f\u89e3\u6790\u306e\u521d\u671f\u6bb5\u968e\u3067\u767b\u5834\u3059\u308b\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u5b9f\u306f\u5fdc\u7528\u6570\u5b66\u306e\u5e83\u5927\u306a\u9818\u57df\u3092\u9759\u304b\u306b\u652f\u3048\u3066\u3044\u308b\u7d50\u679c\u306e\u4e00\u3064\u3067\u3059\u3002\u7269\u7406\u5b66\u3001\u7d4c\u6e08\u5b66\u3001\u7d71\u8a08\u5b66\u306a\u3069\u3067\u3001\u3042\u308b\u91cf\u3092\u5236\u7d04\u306e\u3082\u3068\u3067\u300c\u6700\u5927\u5316\u300d\u3042\u308b\u3044\u306f\u300c\u6700\u5c0f\u5316\u300d\u3059\u308b\u3068\u8ff0\u3079\u308b\u3068\u304d\u3001\u305d\u306e\u80cc\u5f8c\u3067\u306f\u3053\u306e\u5b9a\u7406\u304c\u4fdd\u8a3c\u3059\u308b\u8003\u3048\u65b9\u306b\u975e\u5e38\u306b\u8fd1\u3044\u3082\u306e\u304c\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u9023\u7d9a\u95a2\u6570\u306f<strong>\u5358\u306b\u6709\u754c\u3067\u3042\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u6975\u5024\u3092\u5b9f\u969b\u306b\u9054\u6210\u3059\u308b<\/strong>\u3068\u3044\u3046\u4e8b\u5b9f\u3067\u3059\u3002\n<\/p>\n<p>\n\u76f4\u89b3\u7684\u306b\u306f\u3001\u9023\u7d9a\u306a\u66f2\u7dda\u3092<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\u3068\u3044\u3046\u7dda\u5206\u4e0a\u306b\u63cf\u3051\u3070\u3001\u6700\u3082\u9ad8\u3044\u70b9\u3068\u6700\u3082\u4f4e\u3044\u70b9\u304c\u5b58\u5728\u3059\u308b\u306e\u306f\u300c\u5f53\u7136\u300d\u306e\u3088\u3046\u306b\u601d\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u4eee\u5b9a\u3092\u308f\u305a\u304b\u306b\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u3001\u3053\u306e\u76f4\u89b3\u306f\u5bb9\u6613\u306b\u5d29\u58ca\u3057\u307e\u3059\u3002\u533a\u9593\u3092\u958b\u3051\u3070\u3001\u95a2\u6570\u304c\u9023\u7d9a\u3067\u306a\u3051\u308c\u3070\u3001\u3042\u308b\u3044\u306f\u5b9a\u7fa9\u57df\u304c\u6709\u754c\u3067\u306a\u3051\u308c\u3070\u3001\u6700\u5927\u5024\u3084\u6700\u5c0f\u5024\u306f\u5bb9\u6613\u306b\u300c\u5b58\u5728\u3057\u306a\u304f\u306a\u308b\u300d\u306e\u3067\u3059\u3002Weierstrass \u306e\u5b9a\u7406\u306f\u3001\u3053\u306e\u76f4\u89b3\u3092\u660e\u78ba\u306b\u6574\u7406\u3057\u3001<em>\u3044\u3064<\/em>\u305d\u308c\u3092\u4fe1\u983c\u3067\u304d\u3001<em>\u306a\u305c<\/em>\u305d\u3046\u306a\u306e\u304b\u3092\u6b63\u78ba\u306b\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\n<\/p>\n<p>\n\u7406\u8ad6\u7684\u89b3\u70b9\u304b\u3089\u898b\u308b\u3068\u3001\u3053\u306e\u5b9a\u7406\u306f<strong>\u30b3\u30f3\u30d1\u30af\u30c8\u6027<\/strong>\u3068\u3044\u3046\u6982\u5ff5\u3068\u306e\u6700\u521d\u306e\u672c\u683c\u7684\u306a\u51fa\u4f1a\u3044\u3067\u3059\u3002\u73fe\u4ee3\u7684\u8868\u73fe\u3067\u306f\u3001\u9023\u7d9a\u95a2\u6570\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3092\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3078\u5199\u3059\u3068\u3044\u3046\u3053\u3068\u3092\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\u5b9f\u8df5\u7684\u89b3\u70b9\u3067\u306f\u3001\u3053\u308c\u306f\u4e00\u6b21\u5143\u306e\u6700\u9069\u5316\u554f\u984c\u306b\u89e3\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3078\u3068\u76f4\u7d50\u3057\u3001\u5f8c\u306b\u7d9a\u304f<b>\u5e73\u5747\u5024\u306e\u5b9a\u7406<\/b>\u3084\u3001\u6700\u7d42\u7684\u306b\u306f\u5fae\u7a4d\u5206\u5b66\u306e\u57fa\u672c\u5b9a\u7406\u3092\u843d\u3061\u7740\u3044\u3066\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u91cd\u8981\u306a\u4e00\u90e8\u3068\u306a\u308a\u307e\u3059\u3002\n<\/p>\n<p>\n\u672c\u7bc0\u3067\u306f Weierstrass \u306e\u5b9a\u7406\u3092\u8ff0\u3079\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\u306b\u304a\u3051\u308b\u9023\u7d9a\u6027\u3068\u4e0a\u9650\u516c\u7406\u306e\u6982\u5ff5\u3092\u7528\u3044\u3066\u8a73\u7d30\u306a\u8a3c\u660e\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u672c\u7a3f\u304c\u3001\u5b9a\u7406\u305d\u306e\u3082\u306e\u306e\u5b66\u7fd2\u306b\u3082\u3001\u4ed6\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u305f\u308a\u5177\u4f53\u7684\u306a\u554f\u984c\u3067\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u306e\u5b58\u5728\u3092\u53b3\u5bc6\u306b\u6b63\u5f53\u5316\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u306b\u7acb\u3061\u8fd4\u308b\u305f\u3081\u306e\u78ba\u304b\u306a\u53c2\u7167\u8cc7\u6599\u3068\u306a\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h2>Weierstrass \u306e\u5b9a\u7406\u306e\u8a18\u8ff0<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #e0e0ff;\">\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=N5mSrhJgCds&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u3059\u3079\u3066\u306e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span><\/strong><\/a> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u9023\u7d9a\u3067\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u95a2\u6570\u306f\u6709\u754c\u3067\u3042\u308a\u3001\u6700\u5c0f\u5024\u304a\u3088\u3073\u6700\u5927\u5024 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span> \u3092\u3082\u3064\u3002\u3055\u3089\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span> \u3067\u3042\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\in[m,M]<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h3>\u8a3c\u660e<\/h3>\n<p>\n<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u304c\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067\u9023\u7d9a\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u304c\u6709\u754c\u3067\u3042\u308a\u3001\u3055\u3089\u306b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u9054\u6210\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u8a3c\u660e\u306f\u4ee5\u4e0b\u306e\u4e8c\u3064\u306e\u4e3b\u8981\u90e8\u5206\u306b\u5206\u3051\u3066\u9032\u3081\u307e\u3059\u3002\n<\/p>\n<ul>\n<li>\u307e\u305a\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306e\u9023\u7d9a\u6027\u304c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067\u306e<em>\u4e00\u69d8\u9023\u7d9a\u6027<\/em>\u3092\u5c0e\u304f\u3053\u3068\u3092\u793a\u3057\u3001\u305d\u3053\u304b\u3089\u95a2\u6570\u304c<strong>\u6709\u754c<\/strong>\u3067\u3042\u308b\u3053\u3068\u3092\u7d50\u8ad6\u3065\u3051\u307e\u3059\u3002<\/li>\n<li>\u6b21\u306b\u3001\u4e0a\u9650\u516c\u7406\u3092\u7528\u3044\u3066\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u304c\u533a\u9593\u5185\u3067\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u5b9f\u969b\u306b\u53d6\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 1\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306b\u304a\u3051\u308b\u70b9\u3054\u3068\u306e\u9023\u7d9a\u6027<\/h4>\n<p>\n\u4eee\u5b9a\u3088\u308a\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306f\u5404\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u306b\u304a\u3044\u3066\u9023\u7d9a\u3067\u3059\u3002<span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span>\u2013<span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u306b\u3088\u308b\u9023\u7d9a\u6027\u306e\u5b9a\u7fa9\u306b\u3088\u308c\u3070\u3001\u3053\u308c\u306f\u6b21\u3092\u610f\u5473\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall \\epsilon\\gt 0)(\\exists \\delta(x_0)\\gt 0)\n\n\\big(|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u3053\u3053\u3067\u3001\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u306f\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u306b\u4f9d\u5b58\u3057\u3066\u3088\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u307e\u3059\u3002\u6211\u3005\u306e\u6700\u521d\u306e\u76ee\u6a19\u306f\u3001\u3053\u308c\u3089\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u304b\u3089\u3001\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u306b\u4f9d\u5b58\u3057\u306a\u3044\u5358\u4e00\u306e\u6570 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u3092\u69cb\u6210\u3057\u3001\u533a\u9593\u5168\u4f53\u3067\u4e00\u5ea6\u306b\u6a5f\u80fd\u3059\u308b\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u3067\u3059\u3002\n<\/p>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 2\uff1a<\/b> \u9023\u7d9a\u6027\u306b\u95a2\u9023\u3059\u308b\u958b\u88ab\u8986<\/h4>\n<p>\n\u4efb\u610f\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\\gt 0<\/span><\/span><\/strong> \u3092\u56fa\u5b9a\u3057\u307e\u3059\u3002\u5404\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u306b\u3064\u3044\u3066\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306e\u9023\u7d9a\u6027\u306b\u3088\u308a\u3001\u6b21\u3092\u6e80\u305f\u3059 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)\\gt 0<\/span><\/span><\/strong> \u3092\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u3053\u308c\u3089\u306e\u5024\u3092\u7528\u3044\u3066\u3001\u5404 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u6b21\u306e\u958b\u533a\u9593\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_0}=\\left(x_0-\\frac{\\delta(x_0)}{2},\\,x_0+\\frac{\\delta(x_0)}{2}\\right).\n\n<\/span>\n<\/p>\n<p>\n\u5404 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> \u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> \u306b\u304a\u3051\u308b\u958b\u96c6\u5408\u3067\u3042\u308a\u3001\u3055\u3089\u306b\u65cf\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{I_{x_0}\\}_{x_0\\in[a,b]}\n\n<\/span>\n<\/p>\n<p>\n\u306f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u306e<strong>\u958b\u88ab\u8986<\/strong>\u3092\u6210\u3057\u307e\u3059\u3002\u5b9f\u969b\u3001\u4efb\u610f\u306e\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in[a,b]<\/span><\/span><\/strong> \u306b\u3064\u3044\u3066 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0=y<\/span><\/span><\/strong> \u3068\u53d6\u308c\u3070\u3001\u69cb\u6210\u3088\u308a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in I_y<\/span><\/span><\/strong> \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u533a\u9593\u5185\u306e\u5404\u70b9\u306f\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u958b\u96c6\u5408 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> \u306b\u542b\u307e\u308c\u307e\u3059\u3002\n<\/p>\n<p>\n\u3053\u306e\u958b\u96c6\u5408\u65cf\u306f\u4e00\u822c\u306b\u306f<strong>\u7121\u9650<\/strong>\u96c6\u5408\u3067\u3059\uff08<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u3054\u3068\u306b\u4e00\u3064\u5b58\u5728\u3059\u308b\u305f\u3081\uff09\u3002\u3053\u3053\u3067 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002\n<\/p>\n<p><a name=\"6\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 3\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u3068\u6709\u9650\u90e8\u5206\u88ab\u8986<\/h4>\n<p>\nHeine\u2013Borel \u306e\u5b9a\u7406\u3088\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u306e\u90e8\u5206\u96c6\u5408\u304c\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u306e\u306f\u3001\u305d\u308c\u304c\u9589\u304b\u3064\u6709\u754c\u3067\u3042\u308b\u3068\u304d\u306b\u9650\u308a\u307e\u3059\u3002\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u306f\u9589\u304b\u3064\u6709\u754c\u3067\u3042\u308b\u305f\u3081\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u306e\u5b9a\u7fa9\u3088\u308a\u3001\n<\/p>\n<p>\n<strong>\u3069\u306e\u3088\u3046\u306a<\/strong>\u958b\u88ab\u8986\uff08\u305f\u3068\u3048\u7121\u9650\u500b\u306e\u96c6\u5408\u304b\u3089\u6210\u3063\u3066\u3044\u3066\u3082\uff09\u304b\u3089\u3082\u3001<strong>\u6709\u9650\u90e8\u5206\u88ab\u8986<\/strong>\u3092\u53d6\u308a\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\n<\/p>\n<p>\n\u3053\u306e\u6027\u8cea\u3092\u958b\u88ab\u8986 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{I_{x_0}\\}_{x_0\\in[a,b]}<\/span><\/span><\/strong> \u306b\u9069\u7528\u3059\u308b\u3068\u3001\u3042\u308b\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,\\dots,x_N\\in[a,b]<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066\u3001\u5bfe\u5fdc\u3059\u308b\u958b\u533a\u9593\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_1},\\, I_{x_2},\\,\\dots,\\,I_{x_N}\n\n<\/span>\n<\/p>\n<p>\n\u3053\u306e\u6709\u9650\u90e8\u5206\u88ab\u8986\u306f\u533a\u9593\u5168\u4f53\u3092\u8986\u3044\u7d9a\u3051\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n[a,b]\\subset I_{x_1}\\cup I_{x_2}\\cup\\cdots\\cup I_{x_N}.\n\n<\/span>\n<\/p>\n<p>\n\u3053\u306e\u3088\u3046\u306b\u3001\u7121\u9650\u500b\u306e\u958b\u533a\u9593\u304b\u3089\u6210\u308b\u65cf\u304b\u3089\u3001\u4f9d\u7136\u3068\u3057\u3066 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u5168\u4f53\u3092\u8986\u3046<strong>\u6709\u9650<\/strong>\u500b\u306e\u958b\u533a\u9593\u3060\u3051\u3092\u62bd\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\n<\/p>\n<p><a name=\"7\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 4\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u4f9d\u5b58\u3057\u306a\u3044 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u306e\u69cb\u6210\uff08\u5747\u7b49\u9023\u7d9a\u6027\uff09<\/h4>\n<p>\n\u6709\u9650\u90e8\u5206\u88ab\u8986\u3092\u7528\u3044\u3066\u3001\u6b21\u306e\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\delta=\\min\\left\\{\\frac{\\delta(x_1)}{2},\\frac{\\delta(x_2)}{2},\\dots,\\frac{\\delta(x_N)}{2}\\right\\}.\n\n<\/span>\n<\/p>\n<p>\n\u3053\u308c\u306f\u6709\u9650\u500b\u306e\u6b63\u306e\u6570\u306e\u6700\u5c0f\u5024\u306a\u306e\u3067\u3001\u78ba\u304b\u306b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong> \u3067\u3059\u3002\u3053\u306e <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u304c\u3001\u4efb\u610f\u306e\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u3066\u6a5f\u80fd\u3057\u3001\u3059\u306a\u308f\u3061 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u306b\u4f9d\u5b58\u3057\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\n<\/p>\n<p>\n\u3053\u3053\u3067\u6b21\u3092\u53d6\u308a\u307e\u3059\u3002\n<\/p>\n<ul>\n<li>\u4efb\u610f\u306e\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\u3001<\/li>\n<li><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong> \u3092\u6e80\u305f\u3059 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong>\u3002<\/li>\n<\/ul>\n<p>\n\u958b\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_1},\\dots,I_{x_N}<\/span><\/span><\/strong> \u304c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u3092\u8986\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u306f\u305d\u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u3001\u4f8b\u3048\u3070\u3042\u308b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">j\\in\\{1,\\dots,N\\}<\/span><\/span><\/strong> \u306b\u5bfe\u3057 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong> \u306b\u5c5e\u3057\u307e\u3059\u3002\u5b9a\u7fa9\u3088\u308a\u3001\u3053\u308c\u306f\u6b21\u3092\u610f\u5473\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x_0-x_j|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u3055\u3089\u306b\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/strong> \u306e\u5b9a\u7fa9\u3088\u308a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\le\\frac{\\delta(x_j)}{2}<\/span><\/span><\/strong> \u304c\u6210\u308a\u7acb\u3064\u305f\u3081\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong> \u304b\u3089\u6b21\u304c\u5f93\u3044\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3092\u7528\u3044\u308b\u3068\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_j|\\le |x-x_0|+|x_0-x_j|\n\n\\lt \\frac{\\delta(x_j)}{2}+\\frac{\\delta(x_j)}{2}\n\n=\\delta(x_j).\n\n<\/span>\n<\/p>\n<p>\n<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_j<\/span><\/span><\/strong> \u306b\u304a\u3051\u308b\u9023\u7d9a\u6027\uff08\u8aa4\u5dee <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\/2<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u3066\uff09\u3088\u308a\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x_0-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u304a\u3088\u3073 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u306f\u6b21\u3092\u542b\u610f\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x_0)-f(x_j)|\\lt\\frac{\\epsilon}{2}\n\n\\quad\\text{y}\\quad\n\n|f(x)-f(x_j)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u518d\u3073\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3092\u9069\u7528\u3059\u308b\u3068\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_0)|\n\n\\le |f(x)-f(x_j)| + |f(x_j)-f(x_0)|\n\n\\lt \\frac{\\epsilon}{2}+\\frac{\\epsilon}{2}\n\n=\\epsilon.\n\n<\/span>\n<\/p>\n<p>\n<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u3068 <strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/strong> \u306f\u4efb\u610f\u3067\u3042\u3063\u305f\u305f\u3081\u3001\u6700\u521d\u306b\u56fa\u5b9a\u3057\u305f <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span><\/strong> \u306b\u5bfe\u3057\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u306b\u4f9d\u5b58\u3057\u306a\u3044 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall x\\in[a,b])\n\n\\big(|x-x_0|\\lt\\delta\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u3053\u3053\u3067 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u3092 <strong><span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/strong> \u3068\u66f8\u304d\u63db\u3048\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall \\epsilon\\gt 0)(\\exists \\delta\\gt 0)(\\forall x,y\\in[a,b])\n\n\\big(|x-y|\\lt\\delta\\Rightarrow |f(x)-f(y)|\\lt\\epsilon\\big),\n\n<\/span>\n<\/p>\n<p>\n\u3053\u308c\u306f\u307e\u3055\u306b\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u304c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067<strong>\u4e00\u69d8\u9023\u7d9a<\/strong>\u3067\u3042\u308b\u3068\u3044\u3046\u5b9a\u7fa9\u305d\u306e\u3082\u306e\u3067\u3059\u3002\u4ee5\u964d\u3067\u306f\u3001\u3053\u306e\u7d50\u679c\u3092 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u306e\u5834\u5408\u306b\u9069\u7528\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002\n<\/p>\n<p><a name=\"8\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 5\uff1a<\/b> \u4e00\u69d8\u9023\u7d9a\u6027\u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u306b\u304a\u3051\u308b <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u306e\u6709\u754c\u6027\u3078<\/h4>\n<p>\n\u3053\u3053\u3067\u4e00\u69d8\u9023\u7d9a\u6027\u3092 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u3066\u9069\u7528\u3057\u307e\u3059\u3002\u3059\u308b\u3068\u3001\u3042\u308b\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1\\gt 0<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066\u3001\u4efb\u610f\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in[a,b]<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u6b21\u304c\u6210\u7acb\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-y|\\lt\\delta_1\\Rightarrow |f(x)-f(y)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u6b21\u306b\u3001\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u3092\u9577\u3055\u304c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1<\/span><\/span><\/strong> \u3088\u308a\u5c0f\u3055\u3044\u6709\u9650\u500b\u306e\u90e8\u5206\u533a\u9593\u306b\u5206\u5272\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u6574\u6570 <strong><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/strong> \u3068\u70b9\u5217\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\na = x_0 \\lt x_1 \\lt \\cdots \\lt x_n = b\n\n<\/span>\n<\/p>\n<p>\n\u3092\u53d6\u308a\u3001\u5404 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0,1,\\dots,n-1<\/span><\/span><\/strong> \u306b\u3064\u3044\u3066\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nx_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n\u6b21\u306b\u6709\u9650\u96c6\u5408\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{f(x_0),f(x_1),\\dots,f(x_{n-1})\\}.\n\n<\/span>\n<\/p>\n<p>\n\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u308c\u306f\u6709\u9650\u500b\u306e\u5b9f\u6570\u304b\u3089\u306a\u308b\u96c6\u5408\u306a\u306e\u3067\u3001\u6b21\u3092\u554f\u984c\u306a\u304f\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nC = \\max\\{|f(x_k)| \\;|\\; k=0,1,\\dots,n-1\\}.\n\n<\/span>\n<\/p>\n<p>\n\u3053\u3053\u3067 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C+1<\/span><\/span><\/strong> \u304c\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u5168\u4f53\u306b\u308f\u305f\u308b <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306e\u7d76\u5bfe\u5024\u306e\u4e0a\u754c\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u4efb\u610f\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u3001\u3042\u308b <strong><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[x_k,x_{k+1}]<\/span><\/span><\/strong> \u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u7279\u306b\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_k|\\le x_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u306b\u5bfe\u3059\u308b\u4e00\u69d8\u9023\u7d9a\u6027\u3088\u308a\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_k|\\lt\\delta_1<\/span><\/span><\/strong> \u306a\u3089\u3070\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_k)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3092\u7528\u3044\u308b\u3068\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le |f(x)-f(x_k)| + |f(x_k)| \\lt 1 + |f(x_k)| \\le 1 + C.\n\n<\/span>\n<\/p>\n<p>\n<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u306f\u4efb\u610f\u3067\u3042\u3063\u305f\u305f\u3081\u3001\u6b21\u3092\u7d50\u8ad6\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le C+1 \\quad \\text{para todo } x\\in[a,b],\n\n<\/span>\n<\/p>\n<p>\n\u3059\u306a\u308f\u3061\u3001\u95a2\u6570 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u306f\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067<strong>\u6709\u754c<\/strong>\u3067\u3059\u3002\n<\/p>\n<p><a name=\"9\"><\/a><\/br><\/p>\n<h4><b>\u30b9\u30c6\u30c3\u30d7 6\uff1a<\/b> \u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u306e\u5b58\u5728<\/h4>\n<p>\n\u95a2\u6570\u304c\u533a\u9593\u3067\u53d6\u308b\u5024\u306e\u96c6\u5408\u3092\u6b21\u3067\u5b9a\u7fa9\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nH=\\{f(x)\\;|\\;x\\in[a,b]\\}\\subset\\mathbb{R}.\n\n<\/span>\n<\/p>\n<p>\n<strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u306f\u7a7a\u3067\u306a\u304f\uff08<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u304c\u7a7a\u3067\u306a\u3044\u305f\u3081\uff09\u3001\u3055\u3089\u306b\u6709\u754c\u306a\u306e\u3067\u3001\u4e0a\u9650\u516c\u7406\u306b\u3088\u308a\u6b21\u306e\u5b9f\u6570\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM=\\sup H,\\qquad m=\\inf H.\n\n<\/span>\n<\/p>\n<p>\n\u3053\u3053\u3067 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u304c\u5b9f\u969b\u306b\u95a2\u6570\u306e\u5024\u3068\u3057\u3066\u9054\u6210\u3055\u308c\u308b\u3001\u3059\u306a\u308f\u3061 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1)=M<\/span><\/span><\/strong> \u3068\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u80cc\u7406\u6cd5\u3067\u8a3c\u660e\u3057\u307e\u3059\u3002\n<\/p>\n<p>\n<strong><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/strong> \u304c\u6c7a\u3057\u3066 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u3092\u53d6\u3089\u306a\u3044\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(f(x)\\lt M\\big).\n\n<\/span>\n<\/p>\n<p>\n\u3053\u306e\u4eee\u5b9a\u306e\u4e0b\u3067\u6b21\u306e\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\ng(x)=\\frac{1}{M-f(x)}\n\n<\/span>\n<\/p>\n<p>\n\u4eee\u5b9a\u3088\u308a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-f(x)\\gt 0<\/span><\/span><\/strong> \u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u95a2\u6570\u306f\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u306e\u5168\u3066\u306e\u70b9\u3067\u6b63\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u307e\u305f\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u304c\u9023\u7d9a\u3067\u3042\u308a <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u304c\u5b9a\u6570\u3067\u3042\u308b\u305f\u3081\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/strong> \u3082\u9023\u7d9a\u3067\u3059\u3002\u8a3c\u660e\u306e\u524d\u534a\u3088\u308a\u3001\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u306e\u4efb\u610f\u306e\u9023\u7d9a\u95a2\u6570\u306f\u6709\u754c\u3067\u3042\u308b\u305f\u3081\u3001\u3042\u308b\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N\\gt 0<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3001\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(g(x)\\le N\\big).\n\n<\/span>\n<\/p>\n<p>\n\u7279\u306b\u3001\u3059\u3079\u3066\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u306b\u5bfe\u3057\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\frac{1}{M-f(x)} = g(x)\\le N,\n\n<\/span>\n<\/p>\n<p>\n\u3053\u308c\u306f\u6b21\u3068\u540c\u5024\u3067\u3059\u3002\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM-f(x)\\ge \\frac{1}{N}\n\n\\quad\\Rightarrow\\quad\n\nf(x)\\le M-\\frac{1}{N}.\n\n<\/span>\n<\/p>\n<p>\n\u3064\u307e\u308a\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u306e\u3059\u3079\u3066\u306e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u306e\u5024\u306f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-\\frac{1}{N}<\/span><\/span><\/strong> \u4ee5\u4e0b\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u7279\u306b\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u306e\u4e0a\u9650\u306f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\sup H\\le M-\\frac{1}{N}\\lt M,\n\n<\/span>\n<\/p>\n<p>\n\u3068\u306a\u308a\u3001\u3053\u308c\u306f <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u304c <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u306e\u4e0a\u9650\u3067\u3042\u308b\u3068\u3044\u3046\u5b9a\u7fa9\u306b\u77db\u76fe\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4eee\u5b9a\u306f\u8aa4\u308a\u3067\u3042\u308a\u3001\u3042\u308b\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_1)=M.\n\n<\/span>\n<\/p>\n<p>\n\u5168\u304f\u540c\u69d8\u306e\u8b70\u8ad6\u3092\u4e0b\u9650 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=\\inf H<\/span><\/span><\/strong> \u306b\u9069\u7528\u3059\u308c\u3070\uff08\u4f8b\u3048\u3070 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=-f(x)<\/span><\/span><\/strong> \u3092\u8003\u3048\u308b\u3053\u3068\u3067\uff09\u3001\u3042\u308b\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2\\in[a,b]<\/span><\/span><\/strong> \u304c\u5b58\u5728\u3057\u3066\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_2)=m.\n\n<\/span>\n<\/p>\n<p><a name=\"10\"><\/a><\/br><\/p>\n<h2>\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u306b\u3088\u308b\u89e3\u91c8\u3068\u7d50\u8ad6<\/h2>\n<p>\n\u9023\u7d9a\u95a2\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u304c\u6709\u754c\u3067\u3042\u308a\u3001\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u3067\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u9054\u6210\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002\u73fe\u4ee3\u7684\u306a\u89e3\u6790\u306e\u8a00\u8449\u3067\u306f\u3001\u3053\u308c\u306f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u306b\u304a\u3044\u3066\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u304c\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308a\u3001\u9023\u7d9a\u5199\u50cf\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3092\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3078\u5199\u3059\u3001\u3068\u3044\u3046\u4e8b\u5b9f\u3068\u3057\u3066\u89e3\u91c8\u3055\u308c\u307e\u3059\u3002\n<\/p>\n<p>\n\u7279\u306b\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u304c\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308a\u3001<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u304c <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u4e0a\u3067\u9023\u7d9a\u3067\u3042\u308b\u306a\u3089\u3001\u50cf <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u306f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u90e8\u5206\u96c6\u5408\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u304c\u6709\u754c\u3067\u3042\u308a\u3001\u305d\u306e\u4e2d\u3067\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u304c\u5b9f\u969b\u306b\u9054\u6210\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u3053\u308c\u3053\u305d\u304c Weierstrass \u306e\u5b9a\u7406\u306e\u5185\u5bb9\u306b\u4ed6\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Weierstrass \u306e\u6975\u5024\u5b9a\u7406 \u306a\u305c\u591a\u304f\u306e\u6700\u9069\u5316\u554f\u984c\u306b\u304a\u3044\u3066\u3001\u300c\u6700\u5927\u5024\u306f\u5b58\u5728\u3059\u308b\u300d\u3042\u308b\u3044\u306f\u300c\u5fc5\u305a\u6700\u5c0f\u5024\u304c\u3042\u308b\u300d\u3068\u307b\u3068\u3093\u3069\u5f53\u7136\u306e\u3088\u3046\u306b\u524d\u63d0\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5b9f\u969b\u306b\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u7d50\u8ad6\u3092\u5fc5\u305a\u3057\u3082\u4fdd\u8a3c\u3059\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002Weierstrass \u306e\u5b9a\u7406\u3053\u305d\u304c\u3053\u306e\u7591\u554f\u3092\u89e3\u6c7a\u3059\u308b\u6b20\u3051\u3066\u3044\u305f\u8981\u7d20\u3067\u3042\u308a\u3001\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u9023\u7d9a\u95a2\u6570\u304c\u6709\u754c\u3067\u3042\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u6975\u5024\u3092\u5b9f\u969b\u306b\u9054\u6210\u3059\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u672c\u7a3f\u3067\u306f\u3001\u5b9a\u7406\u306e\u6b63\u78ba\u306a\u8a18\u8ff0\u3092\u78ba\u8a8d\u3057\u3001\u70b9\u3054\u3068\u306e\u9023\u7d9a\u6027\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u6027\u3001\u4e0a\u9650\u516c\u7406\u306b\u57fa\u3065\u304f\u53b3\u5bc6\u306a\u8a3c\u660e\u3092\u4e01\u5be7\u306b\u69cb\u7bc9\u3057\u3001\u3055\u3089\u306b\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u4e0a\u306e\u9023\u7d9a\u95a2\u6570\u3068\u3044\u3046\u73fe\u4ee3\u7684\u67a0\u7d44\u307f\u306b\u3088\u308b\u89e3\u91c8\u306b\u3064\u3044\u3066\u3082\u8ad6\u3058\u307e\u3059\u3002\u8aad\u307f\u7d42\u3048\u308b\u9803\u306b\u306f\u3001\u5358\u306b\u5b9a\u7406\u3092\u6697\u8a18\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u306a\u305c\u305d\u308c\u304c\u6210\u308a\u7acb\u3064\u306e\u304b\u3001\u305d\u3057\u3066\u306a\u305c\u89e3\u6790\u5b66\u3001\u6700\u9069\u5316\u3001\u5fdc\u7528\u30e2\u30c7\u30eb\u306b\u304a\u3044\u3066\u7e70\u308a\u8fd4\u3057\u73fe\u308c\u308b\u306e\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19 Weierstrass \u306e\u5b9a\u7406\u306e\u5185\u5bb9\u3092\u7406\u89e3\u3059\u308b\u3002 \u5b9a\u7406\u306e\u524d\u63d0\uff08\u9023\u7d9a\u95a2\u6570\u304c\u9589\u304b\u3064\u6709\u754c\u306a\u533a\u9593 \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3053\u3068\uff09\u3068\u4e3b\u8981\u7d50\u8ad6\u3067\u3042\u308b\u6709\u754c\u6027\u304a\u3088\u3073\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u306e\u5b58\u5728\u3092\u6b63\u78ba\u306b\u628a\u63e1\u3059\u308b\u3002 \u30b3\u30f3\u30d1\u30af\u30c8\u6027\u306e\u89b3\u70b9\u304b\u3089 Weierstrass \u306e\u5b9a\u7406\u3092\u89e3\u91c8\u3059\u308b\u3002 \u9023\u7d9a\u95a2\u6570\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u96c6\u5408\u3092\u6975\u5024\u304c\u9054\u6210\u3055\u308c\u308b\u96c6\u5408\u3078\u5199\u3059\u3068\u3044\u3046\u73fe\u4ee3\u7684\u8868\u73fe\u3092\u7528\u3044\u3066\u3001 \u306e\u5834\u5408\u3092\u5b9f\u89e3\u6790\u306b\u304a\u3051\u308b\u4e00\u822c\u7684\u67a0\u7d44\u307f\u3068\u7d50\u3073\u4ed8\u3051\u3066\u8ff0\u3079\u308b\u3002 Weierstrass \u306e\u5b9a\u7406\u3068\u6700\u9069\u5316\u554f\u984c\u306e\u95a2\u4fc2\u3092\u7406\u89e3\u3059\u308b\u3002 \u591a\u304f\u306e\u4e00\u5909\u6570\u6700\u9069\u5316\u554f\u984c\u306b\u304a\u3044\u3066\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u306e\u5b58\u5728\u3092\u4fdd\u8a3c\u3059\u308b\u7406\u8ad6\u7684\u57fa\u76e4\u3068\u3057\u3066\u3001\u3053\u306e\u5b9a\u7406\u304c\u679c\u305f\u3059\u5f79\u5272\u3092\u628a\u63e1\u3059\u308b\uff08\u7406\u8ad6\u7684\u72b6\u6cc1\u30fb\u5fdc\u7528\u72b6\u6cc1\u306e\u53cc\u65b9\u3092\u542b\u3080\uff09\u3002 \u76ee\u6b21: \u5e8f\u8ad6 Weierstrass \u306e\u5b9a\u7406\u306e\u8a18\u8ff0 \u8a3c\u660e \u30b9\u30c6\u30c3\u30d7 1\uff1a \u306b\u304a\u3051\u308b\u70b9\u3054\u3068\u306e\u9023\u7d9a\u6027 \u30b9\u30c6\u30c3\u30d7 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