{"id":192,"date":"2019-11-26T03:48:36","date_gmt":"2019-11-26T03:48:36","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=192"},"modified":"2019-11-26T03:48:36","modified_gmt":"2019-11-26T03:48:36","slug":"aops_cp-floor-and-ceiling-functions","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2019\/11\/26\/aops_cp-floor-and-ceiling-functions\/","title":{"rendered":"AoPS_CP: Floor and Ceiling Functions"},"content":{"rendered":"\n<p>Here is what we have met in Problem 10.3 yesterday, about the &#8220;greatest integer less than or equal to x&#8221;. The mathematical name is &#8220;floor function&#8221;. On the other hand, we have a &#8220;ceiling function&#8221;, which is the &#8220;smallest integer greater than or equal to x&#8221;.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function-of-2.31.png\" alt=\"\" class=\"wp-image-193\" width=\"290\" height=\"155\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function-of-2.31.png 545w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function-of-2.31-300x161.png 300w\" sizes=\"(max-width: 290px) 100vw, 290px\" \/><\/figure>\n\n\n\n<p>Please visit this website for detailed information:  <a href=\"https:\/\/www.mathsisfun.com\/sets\/function-floor-ceiling.html\">https:\/\/www.mathsisfun.com\/sets\/function-floor-ceiling.html<\/a> <\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function.png\" alt=\"\" class=\"wp-image-194\" width=\"210\" height=\"87\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function.png 429w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-and-ceiling-function-300x124.png 300w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-graph.png\" alt=\"\" class=\"wp-image-195\" width=\"183\" height=\"211\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-graph.png 296w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/floor-function-graph-260x300.png 260w\" sizes=\"(max-width: 183px) 100vw, 183px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/ceiling-function-graph.png\" alt=\"\" class=\"wp-image-196\" width=\"181\" height=\"207\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/ceiling-function-graph.png 303w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/ceiling-function-graph-262x300.png 262w\" sizes=\"(max-width: 181px) 100vw, 181px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Here is what we have met in Problem 10.3 yesterday, about the &#8220;greatest integer less than or equal to x&#8221;. The mathematical name is &#8220;floor function&#8221;. On the other hand, we have a &#8220;ceiling function&#8221;, which is the &#8220;smallest integer greater than or equal to x&#8221;. Please visit this website for detailed information: https:\/\/www.mathsisfun.com\/sets\/function-floor-ceiling.html<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/192"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=192"}],"version-history":[{"count":1,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/192\/revisions"}],"predecessor-version":[{"id":197,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/192\/revisions\/197"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}