{"id":1733,"date":"2023-10-27T06:00:51","date_gmt":"2023-10-27T04:00:51","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=1733"},"modified":"2023-10-19T13:04:31","modified_gmt":"2023-10-19T11:04:31","slug":"27-oct-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/27-oct-23\/","title":{"rendered":"Hay alg\u00fan n\u00famero real entre 2 y 3"},"content":{"rendered":"<p>Demostrar con Lean4 que hay alg\u00fan n\u00famero real entre 2 y 3.<\/p>\n<p>Para ello, completar la siguiente teor\u00eda de Lean4:<\/p>\n<pre lang=\"lean\">\nimport Mathlib.Data.Real.Basic\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nby sorry\n<\/pre>\n<p><!--more--><\/p>\n<p><b>Demostraci\u00f3n en lenguaje natural<\/b><\/p>\n<p><br \/>\nPuesto que &#92;(2 &lt; 5\/2 &lt; 3&#92;), basta elegir &#92;(5\/2&#92;).<\/p>\n<p><b>Demostraciones con Lean4<\/b><\/p>\n<pre lang=\"lean\">\nimport Mathlib.Data.Real.Basic\n\n-- 1\u00aa demostraci\u00f3n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nby\n  have h : 2 < (5 : \u211d) \/ 2 \u2227 (5 : \u211d) \/ 2 < 3 :=\n    by norm_num\n  show \u2203 x : \u211d, 2 < x \u2227 x < 3\n  exact Exists.intro (5 \/ 2) h\n\n-- 2\u00aa demostraci\u00f3n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nby\n  have h : 2 < (5 : \u211d) \/ 2 \u2227 (5 : \u211d) \/ 2 < 3 :=\n    by norm_num\n  show \u2203 x : \u211d, 2 < x \u2227 x < 3\n  exact \u27e85 \/ 2, h\u27e9\n\n-- 3\u00aa demostraci\u00f3n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nby\n  use 5 \/ 2\n  norm_num\n\n-- 4\u00aa demostraci\u00f3n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\n\u27e85 \/ 2, by norm_num\u27e9\n<\/pre>\n<p><b>Demostraciones interactivas<\/b><\/p>\n<p>Se puede interactuar con las demostraciones anteriores en <a href=\"https:\/\/live.lean-lang.org\/#url=https:\/\/raw.githubusercontent.com\/jaalonso\/Calculemus2\/main\/src\/Existencia_de_valor_intermedio.lean\" rel=\"noopener noreferrer\" target=\"_blank\">Lean 4 Web<\/a>.<\/p>\n<p><b>Referencias<\/b><\/p>\n<ul>\n<li> J. Avigad y P. Massot. <a href=\"https:\/\/bit.ly\/3U4UjBk\">Mathematics in Lean<\/a>, p. 28.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar con Lean4 que hay alg\u00fan n\u00famero real entre 2 y 3. Para ello, completar la siguiente teor\u00eda de Lean4: import Mathlib.Data.Real.Basic example : \u2203 x : \u211d, 2 < x \u2227 x < 3 := by sorry\n<\/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,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":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":[1],"tags":[297,286,287],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1733"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/comments?post=1733"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1733\/revisions"}],"predecessor-version":[{"id":1734,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1733\/revisions\/1734"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=1733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=1733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=1733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}