{"id":489,"date":"2022-11-23T12:04:16","date_gmt":"2022-11-23T03:04:16","guid":{"rendered":"https:\/\/tako.nakano.net\/blog\/?p=489"},"modified":"2022-11-23T12:04:16","modified_gmt":"2022-11-23T03:04:16","slug":"infinite-tetration","status":"publish","type":"post","link":"https:\/\/tako.nakano.net\/blog\/2022\/11\/infinite-tetration\/","title":{"rendered":"sqrt(2) \u306e sqrt(2) \u306e sqrt(2) \u2026 \u4e57\u4e57\u4e57"},"content":{"rendered":"<p>\u7121\u9650\u30c6\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/p>\n<p>\u221a2\u306e\u80a9\u306b\u7121\u9650\u306b\u221a2\u3092\u4e57\u305b\u305f\u3089\u306a\u305c2\u306b\u306a\u308b\u306e\u304b<br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0\">https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0<\/a><\/p>\n<p>\u3068\u3044\u3046\u52d5\u753b\u304c\u3042\u3063\u305f\uff0e<br \/>\n\u30b3\u30e1\u30f3\u30c8\u306b<\/p>\n<blockquote>\n<p>@y2q588<br \/>\n\u7b2c\u4e00\u611f\u306f\u5e73\u5747\u5024\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066f(x)=sqrt(2)^x\u304c\u7e2e\u5c0f\u5199\u50cf\u3068\u306a\u308b\u7bc4\u56f2\u3092\u6c42\u3081\u3066\u7d76\u5bfe\u53ce\u675f\u3092\u793a\u3059&#8230;\u3068\u304b\u8003\u3048\u305f\u3051\u3069\uff0c\u5e30\u7d0d\u6cd5\u3067\u3088\u304b\u3063\u305f\u306e\u304b\uff0e<br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&amp;lc=Ugz_TsCbfobpCnt_TW54AaABAg\">https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&#038;lc=Ugz_TsCbfobpCnt_TW54AaABAg<\/a><\/p>\n<p>@user-fy3un1wz3b<br \/>\n\u3053\u308c\u5e73\u5747\u5024\u306e\u5b9a\u7406\u4f7f\u3063\u3066\u8a3c\u660e\u3067\u304d\u305d\u3046\uff1f<br \/>\nan\u30682\u306e\u9593\u306e\u5897\u52a0\u91cf\u3092\u8003\u3048\u3066\u3001\u3001<br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&amp;lc=Ugx2aoynqYoj4SSrnvZ4AaABAg\">https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&#038;lc=Ugx2aoynqYoj4SSrnvZ4AaABAg<\/a><\/p>\n<p>@Mega11041104<br \/>\n\u305d\u308c\u5341\u5206\u6761\u4ef6\u3067\u3059\u3088\u306d\u3002\u3060\u304b\u3089X\uff1d2\u3067\u3042\u308b\u5fc5\u8981\u6027\u304c\u793a\u3055\u308c\u3066\u306a\u3044\u3002\u3088\u308a\u5177\u4f53\u7684\u306b\u3044\u3048\u3070X\uff1d1.9\u8fba\u308a\u3067x =(\u221a2)^x\u3092\u6e80\u305f\u3059\u5024\u304c\u51fa\u3066\u304d\u305f\u3089\u3069\u3046\u3059\u308b\u3093\u3067\u3059\u304b\uff1f\u305d\u308c\u3082\u8907\u6570\u306e\u5024\u304c\u5b58\u5728\u3057\u3066\u305f\u308a\u3057\u305f\u3089\u3069\u3046\u3057\u307e\u3059\u304b\uff1f<br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&amp;lc=UgyTkoal2aUA1K2RyMN4AaABAg.9ijLvnPXkRn9ikip6fHEGf\">https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&#038;lc=UgyTkoal2aUA1K2RyMN4AaABAg.9ijLvnPXkRn9ikip6fHEGf<\/a><\/p>\n<p>@dttjjm287<br \/>\n\u6f38\u5316\u5f0f\u3067\u6975\u9650\u3092\u53d6\u308b\u6642\u3001y=x\u3068y=Sqrt[2]^x\u304c\u70b9\u5217\u9023\u7d9a\u3067\u3042\u308b\u4e8b\u3092\u4f7f\u3063\u3066\u308b\u306d\uff0e<br \/>\n\u6f38\u5316\u5f0f\u306f\u4efb\u610f\u306e\u81ea\u7136\u6570\u306b\u5bfe\u3057\u3066\u6210\u308a\u7acb\u3064\u7b49\u5f0f\u3067\u3042\u3063\u3066\u3001\u5145\u5206\u5927\u304d\u3044\u81ea\u7136\u6570\u306e\u6642\u306b\u3042\u308b\u4f4d\u76f8\u3067\u6e2c\u3063\u305f\u6642\u306b\u8fd1\u3044\u3068\u3053\u308d\u306b\u3042\u308b\u70b9(\u6975\u9650\u70b9)\u3092\u3044\u3064\u3067\u3082\u4ee3\u5165\u3067\u304d\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u305f\u3044\uff0e<br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&amp;lc=UgzErbYLhe0fISFBqh54AaABAg\">https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0&#038;lc=UgzErbYLhe0fISFBqh54AaABAg<\/a><\/p>\n<\/blockquote>\n<p>\u3053\u3046\u3044\u3046\u8a71\u304c\u51fa\u3066\u3044\u308b\uff0e\u9ad8\u6821\u6570\u5b66\u3067\u666e\u901a\u306b\u793a\u305b\u308b\u306e\u3067\u793a\u305d\u3046\uff0e<\/p>\n<p>Wikipedia \u306e \u30c6\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 \u306b\u306f<\/p>\n<blockquote>\n<p>\u3053\u308c\u304c e\u2212e \u2264 x \u2264 e1\/e \uff08\u304a\u3088\u305d 0.066 \u304b\u3089 1.44\uff09\u306e\u7bc4\u56f2\u3067\u53ce\u675f\u3059\u308b\u3053\u3068\u306f\u30aa\u30a4\u30e9\u30fc\u306b\u3088\u3063\u3066\u793a\u3055\u308c\u305f[12]\u3002<\/p>\n<\/blockquote>\n<p>\u3068\u3042\u3063\u3066\uff0c<br \/>\n<a href=\"http:\/\/eulerarchive.maa.org\/\/docs\/originals\/E532.pdf\">http:\/\/eulerarchive.maa.org\/\/docs\/originals\/E532.pdf<\/a><br \/>\n\u306e 35,36,37 \u30da\u30fc\u30b8\u76ee\u306b\u4e0d\u7b49\u5f0f\u306f\u3042\u308b\u306e\u3060\u304c\uff0c\u53ce\u675f\u3092\u793a\u3057\u3066\u3044\u308b\u306e\u304c\u3069\u3046\u3044\u3046\u8ad6\u7406\u304b\u306f\u3055\u3063\u3071\u308a\u308f\u304b\u3089\u3093\uff0e<\/p>\n<p>\u3067\uff0c\u8a3c\u660e\u3092\u66f8\u3053\u3046\u3068\u3057\u3066\u3044\u305f\u3093\u3060\u304c\uff0c\u5e83\u5cf6\u5927\u5b66\u7406\u7cfb2022\u5e74\u7b2c5\u554f\u304c\u307e\u3055\u306b\u305d\u308c\u3089\u3057\u3044\uff0e<\/p>\n<p>\u540c\u5fd7\u793e2011\u7406\u7cfb\uff0c\u798f\u5cf6\u770c\u7acb\u533b\u79d1\u5927\u5b662019\u3082\u985e\u984c\u3068\u306e\u3053\u3068\uff0e<\/p>\n<p>2022\u5e74 04\u6708 09\u65e5<br \/>\n\u5e83\u5cf6\u5927\u5b66\u7406\u7cfb2022\u5e74\u7b2c\uff15\u554f<br \/>\n<a href=\"https:\/\/mathmathmass.exblog.jp\/31149281\/\">https:\/\/mathmathmass.exblog.jp\/31149281\/<\/a><\/p>\n<p>\u306b\uff0c\u6570\u5217\u306e\u6975\u9650\u3092\u8003\u3048\u308b\u554f\u984c\u3068\u3057\u3066\u89e3\u6cd5\u3068\u3068\u3082\u306b\u7d39\u4ecb\u3055\u308c\u3066\u3044\u308b\uff0e<\/p>\n<p>\u88dc\u8db3\u4e8b\u9805\u3068\u3057\u3066<\/p>\n<p><a href=\"https:\/\/tako.nakano.net\/blog\/wp-content\/uploads\/2022\/11\/sqrt_2_graph.png\"><img decoding=\"async\" src=\"https:\/\/tako.nakano.net\/blog\/wp-content\/uploads\/2022\/11\/sqrt_2_graph.png\" alt=\"\" \/><\/a><\/p>\n<p>3\u672c\u306e\u76f4\u7dda\u306f\uff0c<\/p>\n<ul>\n<li>y = x green<\/li>\n<li>y = sqrt(2) ^x red<\/li>\n<li>y = (ln 2) x + 2 ln 2 blue<\/li>\n<\/ul>\n<p>\u3067\u3042\u308b\uff0e<\/p>\n<p>\u88dc\u8db3\u3092\u3057\u3066\u304a\u304f\uff0e<\/p>\n<p>a_0 = 1 \u3068\u3057\u305f\u3068\u304d\uff0c\u70b9 A \u304b\u3089\u30b9\u30bf\u30fc\u30c8\u3057\uff0c\u70b9 B \u306e y \u5ea7\u6a19\u304c sqrt(2) \u3067\u3042\u308b\uff0e\u305d\u306e\u307e\u307e\u76f4\u7dda y = x \u306b\u79fb\u52d5\u3055\u305b\u3066\u70b9 C \u3092\u5f97\u3066\uff0c\u70b9 C \u306e x \u5ea7\u6a19\u304c sqrt(2) \u3068\u306a\u308b\u2026\u30682\u7dda\u306e\u9593\u3092 \u2191\u2192 \u2191\u2192 \u2191\u2192 \u2026 \u3068\u8fbf\u3063\u3066\u3044\u304f\u3068 x \u5ea7\u6a19\u3092\u5f97\u7d9a\u3051\u305f\u6570\u5217\u304c\u3061\u3087\u3046\u3069 a_n \u3068\u540c\u3058\u306b\u306a\u308b\uff0e<\/p>\n<p>\u59cb\u70b9\u3092 (2, 2), (4, 4) \u306b\u3068\u308b\u3068\uff0c\u305d\u306e\u5834\u304b\u3089\u52d5\u304b\u306a\u3044\u306e\u3067\uff0c\u3053\u308c\u3089\u306f\u4e0d\u52d5\u70b9\u3068\u547c\u3070\u308c\u308b\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7121\u9650\u30c6\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 \u221a2\u306e\u80a9\u306b\u7121\u9650\u306b\u221a2\u3092\u4e57\u305b\u305f\u3089\u306a\u305c2\u306b\u306a\u308b\u306e\u304b https:\/\/www.youtube.com\/watch?v=LABUpfm-rF0 \u3068\u3044\u3046\u52d5\u753b\u304c\u3042\u3063\u305f\uff0e \u30b3\u30e1\u30f3\u30c8\u306b @y2q588 \u7b2c\u4e00\u611f\u306f\u5e73\u5747\u5024 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[23],"tags":[],"class_list":["post-489","post","type-post","status-publish","format-standard","hentry","category-math"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4dIdP-7T","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/posts\/489","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/comments?post=489"}],"version-history":[{"count":2,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/posts\/489\/revisions"}],"predecessor-version":[{"id":492,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/posts\/489\/revisions\/492"}],"wp:attachment":[{"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/media?parent=489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/categories?post=489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tako.nakano.net\/blog\/wp-json\/wp\/v2\/tags?post=489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}