{"id":223,"date":"2011-12-03T00:17:22","date_gmt":"2011-12-02T15:17:22","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=223"},"modified":"2021-10-30T09:58:33","modified_gmt":"2021-10-30T00:58:33","slug":"wsr200901","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr200901\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52009\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5b9f\u6570 \\(x\\) \u306b\u5bfe\u3057\u3066, \\(x\\) \u4ee5\u4e0b\u306e\u6700\u5927\u306e\u6574\u6570\u3092 \\([x]\\) \u3067\u8868\u3059. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(\\dfrac{14}{3} \\lt x \\lt 5\\) \u306e\u3068\u304d, \\(\\left[ \\dfrac{3}{7}x \\right] -\\left[ \\dfrac{3}{7} [x] \\right]\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u3059\u3079\u3066\u306e\u5b9f\u6570 \\(x\\) \u306b\u3064\u3044\u3066, \\(\\left[ \\dfrac{1}{2}x \\right] -\\left[ \\dfrac{1}{2} [x] \\right] =0\\) \u3092\u793a\u305b.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \u5b9f\u6570 \\(x\\) \u306b\u3064\u3044\u3066, \\(\\left[ \\dfrac{1}{n}x \\right] -\\left[ \\dfrac{1}{n} [x] \\right]\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(\\dfrac{14}{3} \\lt x \\lt 5\\) \u3088\u308a , \\(2 \\lt \\dfrac{3}{7}x \\lt \\dfrac{15}{7}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left[ \\dfrac{3}{7}x \\right] -\\left[ \\dfrac{3}{7} [x] \\right] & = 2 -\\left[ \\dfrac{3}{7} \\cdot 4 \\right] \\\\\r\n& = 2 -1 = \\underline{1}\r\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u3059\u3079\u3066\u306e\u5b9f\u6570 \\(x\\) \u306f, \u3042\u308b\u6574\u6570 \\(m\\) \u3092\u7528\u3044\u3066<\/p>\r\n<ul>\r\n<li><p>\\(2m \\leqq x \\lt 2m+1\\)<\/p><\/li>\r\n<li><p>\\(2m+1 \\leqq x \\lt 2m+2\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u306e\u3044\u305a\u308c\u304b\u306b\u5c5e\u3059\u308b\u3053\u3068\u306b\u306a\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(2m \\leqq x \\lt 2m+1\\) \u306e\u3068\u304d<br \/>\r\n\\(m \\leqq \\dfrac{x}{2} \\lt m+\\dfrac{1}{2}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left[ \\dfrac{1}{2}x \\right] -\\left[ \\dfrac{1}{2} [x] \\right] & = m -\\left[ \\dfrac{1}{2} \\cdot 2m \\right] \\\\\r\n& = m -m =0\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(2m+1 \\leqq x \\lt 2m+2\\) \u306e\u3068\u304d<br \/>\r\n\\(m +\\dfrac{1}{2} \\leqq \\dfrac{x}{2} \\lt m+1\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left[ \\dfrac{1}{2}x \\right] -\\left[ \\dfrac{1}{2} [x] \\right] & = m -\\left[ \\dfrac{1}{2} \\cdot (2m+1) \\right] \\\\\r\n& = m -m =0\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n<p><strong>(3)<\/strong><\/p>\r\n<p>\u3059\u3079\u3066\u306e\u5b9f\u6570 \\(x\\) \u306f, \u3042\u308b\u6574\u6570 \\(m , i \\ ( i = 0, 1, \\cdots , n-1 )\\) \u3092\u7528\u3044\u3066\r\n\\[\r\nmn+i \\leqq x \\lt mn+i+1\r\n\\]\r\n\u306e\u3044\u305a\u308c\u304b\u306b\u5c5e\u3059\u308b\u3053\u3068\u306b\u306a\u308b.<br \/>\r\n\u3053\u306e\u3068\u304d, \\(m +\\dfrac{i}{n} \\leqq \\dfrac{x}{n} \\lt m+\\dfrac{i+1}{n}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left[ \\dfrac{1}{n}x \\right] -\\left[ \\dfrac{1}{n} [x] \\right] & = m -\\left[ \\dfrac{1}{2} \\cdot (nm+i) \\right] \\\\\r\n& = m -m = \\underline{0}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(x\\) \u306b\u5bfe\u3057\u3066, \\(x\\) \u4ee5\u4e0b\u306e\u6700\u5927\u306e\u6574\u6570\u3092 \\([x]\\) \u3067\u8868\u3059. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\\(\\dfrac{14}{3} \\lt x \\lt 5\\) \u306e\u3068\u304d, \\(\\left[ \\dfrac{3 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/wsr200901\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[36],"tags":[147,15],"class_list":["post-223","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2009","tag-waseda_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=223"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/223\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}