{"id":186,"date":"2010-01-16T11:21:00","date_gmt":"2010-01-16T14:21:00","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/2010\/01\/o-paradoxo-do-monte\/"},"modified":"2010-01-16T11:21:00","modified_gmt":"2010-01-16T14:21:00","slug":"o-paradoxo-do-monte","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2010\/01\/o-paradoxo-do-monte\/","title":{"rendered":">O Paradoxo do Monte"},"content":{"rendered":"

><\/p>\n

Um simples gr\u00e3o de areia n\u00e3o \u00e9 um monte de areia. Isso \u00e9 \u00f3bvio. Um “monte” \u00e9 uma cole\u00e7\u00e3o de coisas e \u00e9 preciso muitas coisas para se ter um monte <\/i>delas. Assim, dois gr\u00e3os de areia ainda n\u00e3o s\u00e3o um monte de areia por que um monte \u00e9 muito mais que um par de coisas.<\/p>\n

Entretanto, seja quais forem as coisas, o conceito de “monte” \u00e9 confuso e incerto. N\u00e3o h\u00e1 um n\u00famero certo, um limite preciso, a partir do qual uma cole\u00e7\u00e3o de coisas se torna um “monte”. N\u00e3o \u00e9 como se 38 gr\u00e3os de areia formassem um monte, mas 37 ainda n\u00e3o fossem um monte.<\/p>\n

Esta \u00e9 a origem do Paradoxo dos Montes. <\/p>\n

Suponha que tenhamos um milh\u00e3o de gr\u00e3os de areia. Um milh\u00e3o de gr\u00e3os de areia formam, inquestion\u00e1vel-, indubit\u00e1vel-, definitivamente, um monte de areia.<\/p>\n

<\/a><\/p>\n

Mas como n\u00e3o h\u00e1 n\u00famero preciso para definir o que \u00e9 um monte de areia \u2014 ou de qualquer outra coisa \u2014, n\u00f3s poder\u00edamos tirar um <\/i>gr\u00e3o de areia do nosso monte milion\u00e1rio e ele ainda seria um monte, s\u00f3 que com 999.999 gr\u00e3os de areia.<\/p>\n

Mas se \u00e9 assim, ent\u00e3o podemos, igualmente, repetir a retirada de um <\/i>gr\u00e3o de areia outras 999.998 vezes e o que ter\u00edamos no final seria o qu\u00ea? Um monte ou um n\u00e3o-monte?<\/p>\n

N\u00f3s t\u00ednhamos um monte de gr\u00e3os de areia no come\u00e7o deste exemplo. E tudo o que fizemos foi retirar, um por um<\/i>, os gr\u00e3os de areia do monte. Ora, retirar apenas um <\/i>gr\u00e3o n\u00e3o faz do monte um n\u00e3o-monte, mesmo que isso se torne um processo. Eu poderia tirar um gr\u00e3o agora, um daqui a cinco minutos, outro daqui a 10 anos, n\u00e3o importa.<\/p>\n

No fim do processo, independente do ritmo do processo e da quantia de gr\u00e3os que tivermos, s\u00f3 podemos ter um monte. Mas, tamb\u00e9m ao fim do processo, o que temos \u00e9 apenas um <\/i>gr\u00e3o de areia e, como n\u00f3s j\u00e1 sabemos, um gr\u00e3o n\u00e3o pode ser um monte<\/i>.<\/p>\n

Portanto, um \u00fanico e simples gr\u00e3o \u00e9, ao mesmo tempo<\/i>, um monte e um n\u00e3o-monte. <\/div>\n","protected":false},"excerpt":{"rendered":"

> Um simples gr\u00e3o de areia n\u00e3o \u00e9 um monte de areia. Isso \u00e9 \u00f3bvio. Um “monte” \u00e9 uma cole\u00e7\u00e3o de coisas e \u00e9 preciso muitas coisas para se ter um monte delas. Assim, dois gr\u00e3os de areia ainda n\u00e3o s\u00e3o um monte de areia por que um monte \u00e9 muito mais que um par […]<\/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":[198,238,254],"tags":[],"class_list":["post-186","post","type-post","status-publish","format-standard","hentry","category-logica","category-numeros","category-paradoxos"],"yoast_head":"\n>O Paradoxo do Monte - 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\/2010\/01\/o-paradoxo-do-monte\/\" \/>\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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\">O Paradoxo do Monte\",\"datePublished\":\"2010-01-16T14:21:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/\"},\"wordCount\":377,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"articleSection\":[\"l\u00f3gica\",\"n\u00fameros\",\"paradoxos\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2010\\\/01\\\/o-paradoxo-do-monte\\\/\",\"name\":\">O Paradoxo do Monte - 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