{"id":2777,"date":"2012-05-14T21:30:15","date_gmt":"2012-05-15T00:30:15","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=2777"},"modified":"2012-05-14T21:30:15","modified_gmt":"2012-05-15T00:30:15","slug":"dobro-ou-metade","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/","title":{"rendered":"Dobro ou metade?"},"content":{"rendered":"<p align=\"justify\">Mais um curioso paradoxo divisado pelo <em>matem\u00e1gico<\/em> Raymond Smullyan. Considere dois inteiros positivos, <span style=\"font-family: Georgia\"><strong>x<\/strong><\/span> e <span style=\"font-family: Georgia\"><strong>y<\/strong><\/span>. Um \u00e9 o dobro do outro, mas n\u00e3o sabemos qual \u00e9. Assim, conclui-se que:<\/p>\n<ul>\n<li>\n<div align=\"justify\">Se <strong><span style=\"font-family: Georgia\">x<\/span><\/strong> \u00e9 maior que <strong><span style=\"font-family: Georgia\">y<\/span><\/strong>, segue-se que <strong><span style=\"font-family: Georgia\">x = 2y<\/span><\/strong> e a diferen\u00e7a entre <strong><span style=\"font-family: Georgia\">x<\/span><\/strong> e <strong><span style=\"font-family: Georgia\">y<\/span> <\/strong>\u00e9 igual a <strong><span style=\"font-family: Georgia\">y<\/span><\/strong>. Por outro lado, se <strong><span style=\"font-family: Georgia\">y<\/span><\/strong> \u00e9 o maior valor, ent\u00e3o <strong><span style=\"font-family: Georgia\">x = 0,5y<\/span><\/strong> e a diferen\u00e7a entre as inc\u00f3gnitas \u00e9 expressa por <strong><span style=\"font-family: Georgia\">y &#8211; 0,5y = 0,5y<\/span><\/strong>. Como <strong><span style=\"font-family: Georgia\">y<\/span><\/strong> \u00e9 maior que <strong><span style=\"font-family: Georgia\">0,5y<\/span><\/strong>, podemos dizer genericamente que, se <strong><span style=\"font-family: Georgia\">x &gt; y<\/span><\/strong>, a <em>diferen\u00e7a de <\/em><span style=\"font-family: Georgia\"><strong>x<\/strong><\/span><em> e <\/em><span style=\"font-family: Georgia\"><strong>y<\/strong><\/span> \u00e9 <strong>maior<\/strong> do que <em>a diferen\u00e7a de <\/em><span style=\"font-family: Georgia\"><strong>y<\/strong><\/span><em> e <\/em><span style=\"font-family: Georgia\"><strong>x<\/strong><\/span>, se<strong> <span style=\"font-family: Georgia\">y &gt; x<\/span><\/strong>.<\/div>\n<\/li>\n<li>\n<div align=\"justify\">Se <strong><span style=\"font-family: Georgia\"><em>d<\/em><\/span><\/strong> \u00e9 a diferen\u00e7a entre <strong><span style=\"font-family: Georgia\">x<\/span> <\/strong>e <strong><span style=\"font-family: Georgia\">y<\/span><\/strong>, isso \u00e9 o mesmo que dizer que <strong><em><span style=\"font-family: Georgia\">d<\/span><\/em><\/strong> tem o mesmo valor do menor n\u00famero. Assim, geralmente, o <em>excesso de <\/em><span style=\"font-family: Georgia\"><strong>x<\/strong><\/span><em> em rela\u00e7\u00e3o a <\/em><span style=\"font-family: Georgia\"><strong>y<\/strong><\/span>, se <strong><span style=\"font-family: Georgia\">x &gt; y<\/span><\/strong>, \u00e9 <strong>igual<\/strong> ao <em>excesso de <\/em><span style=\"font-family: Georgia\"><strong>y<\/strong><\/span><em> em rela\u00e7\u00e3o a <\/em><span style=\"font-family: Georgia\"><strong>x<\/strong><\/span>, se <span style=\"font-family: Georgia\"><strong>y &gt; x<\/strong><\/span>.<\/div>\n<\/li>\n<\/ul>\n<p align=\"justify\">As duas conclus\u00f5es poss\u00edveis est\u00e3o em clara contradi\u00e7\u00e3o. Qual \u00e9 o problema?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mais um curioso paradoxo divisado pelo matem\u00e1gico Raymond Smullyan. Considere dois inteiros positivos, x e y. Um \u00e9 o dobro do outro, mas n\u00e3o sabemos qual \u00e9. Assim, conclui-se que: Se x \u00e9 maior que y, segue-se que x = 2y e a diferen\u00e7a entre x e y \u00e9 igual a y. Por outro lado, [&hellip;]<\/p>\n","protected":false},"author":486,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[198,203,254],"tags":[],"class_list":["post-2777","post","type-post","status-publish","format-standard","hentry","category-logica","category-matematica","category-paradoxos"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Dobro ou metade? - hypercubic<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Renato Pincelli\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\"Dobro ou metade?\",\"datePublished\":\"2012-05-15T00:30:15+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/\"},\"wordCount\":181,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"articleSection\":[\"l\u00f3gica\",\"matem\u00e1tica\",\"paradoxos\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/\",\"name\":\"Dobro ou metade? - hypercubic\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#website\"},\"datePublished\":\"2012-05-15T00:30:15+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/05\\\/dobro-ou-metade\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"In\u00edcio\",\"item\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Dobro ou metade?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#website\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/\",\"name\":\"hypercubic\",\"description\":\"um hyperespa\u00e7o de ideias\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\",\"name\":\"hypercubic\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/wp-content\\\/uploads\\\/sites\\\/249\\\/2022\\\/11\\\/cropped-Capa-do-Facebook-851x315-px.-1.png\",\"contentUrl\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/wp-content\\\/uploads\\\/sites\\\/249\\\/2022\\\/11\\\/cropped-Capa-do-Facebook-851x315-px.-1.png\",\"width\":197,\"height\":211,\"caption\":\"hypercubic\"},\"image\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/hypercubicBR\\\/\",\"https:\\\/\\\/www.instagram.com\\\/hypercubic.blog\\\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\",\"name\":\"Renato Pincelli\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g\",\"caption\":\"Renato Pincelli\"},\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/author\\\/hypercubic\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Dobro ou metade? - hypercubic","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/","twitter_misc":{"Escrito por":"Renato Pincelli","Est. tempo de leitura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/#article","isPartOf":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/"},"author":{"name":"Renato Pincelli","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#\/schema\/person\/c7be1e2811d061a75d3b4f4960eb53bd"},"headline":"Dobro ou metade?","datePublished":"2012-05-15T00:30:15+00:00","mainEntityOfPage":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/"},"wordCount":181,"commentCount":0,"publisher":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#organization"},"articleSection":["l\u00f3gica","matem\u00e1tica","paradoxos"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/","url":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/","name":"Dobro ou metade? - hypercubic","isPartOf":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#website"},"datePublished":"2012-05-15T00:30:15+00:00","breadcrumb":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/05\/dobro-ou-metade\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"In\u00edcio","item":"https:\/\/www.blogs.unicamp.br\/hypercubic\/"},{"@type":"ListItem","position":2,"name":"Dobro ou metade?"}]},{"@type":"WebSite","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#website","url":"https:\/\/www.blogs.unicamp.br\/hypercubic\/","name":"hypercubic","description":"um hyperespa\u00e7o de ideias","publisher":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.blogs.unicamp.br\/hypercubic\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#organization","name":"hypercubic","url":"https:\/\/www.blogs.unicamp.br\/hypercubic\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#\/schema\/logo\/image\/","url":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-content\/uploads\/sites\/249\/2022\/11\/cropped-Capa-do-Facebook-851x315-px.-1.png","contentUrl":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-content\/uploads\/sites\/249\/2022\/11\/cropped-Capa-do-Facebook-851x315-px.-1.png","width":197,"height":211,"caption":"hypercubic"},"image":{"@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/hypercubicBR\/","https:\/\/www.instagram.com\/hypercubic.blog\/"]},{"@type":"Person","@id":"https:\/\/www.blogs.unicamp.br\/hypercubic\/#\/schema\/person\/c7be1e2811d061a75d3b4f4960eb53bd","name":"Renato Pincelli","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/secure.gravatar.com\/avatar\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/ea6f8dd90510e820f465bc6a0210a398696be86dc9446fbf6420603bafe2a9fb?s=96&d=retro&r=g","caption":"Renato Pincelli"},"url":"https:\/\/www.blogs.unicamp.br\/hypercubic\/author\/hypercubic\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/posts\/2777","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/users\/486"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/comments?post=2777"}],"version-history":[{"count":0,"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/posts\/2777\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/media?parent=2777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/categories?post=2777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/hypercubic\/wp-json\/wp\/v2\/tags?post=2777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}