{"id":262,"date":"2014-05-12T04:00:20","date_gmt":"2014-05-12T02:00:20","guid":{"rendered":"http:\/\/xmau.com\/wp\/ilpost\/?p=262"},"modified":"2022-10-11T13:01:45","modified_gmt":"2022-10-11T11:01:45","slug":"aritmetica-con-linfinito-pillole","status":"publish","type":"post","link":"https:\/\/xmau.com\/ilpost\/2014\/05\/12\/aritmetica-con-linfinito-pillole\/","title":{"rendered":"Aritmetica con l&#8217;infinito [Pillole]"},"content":{"rendered":"<p>In genere si dice di prendere molte precauzioni quando si fanno operazioni con l&#8217;infinito, perch\u00e9 le regole normali dell&#8217;aritmetica non si applicano. Ma basta un po&#8217; di attenzione e si pu\u00f2 fare di tutto. Non ci credete? Eccovi un esempio grafico.<br \/>\nPartiamo da un&#8217;uguaglianza di quelle che non sono ammesse dalla matematica usuale:<br \/>\n<a href=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf1.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"263\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2014\/05\/12\/aritmetica-con-linfinito-pillole\/inf1\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf1.jpg?fit=375%2C194&amp;ssl=1\" data-orig-size=\"375,194\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"inf1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf1.jpg?fit=375%2C194&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf1.jpg?resize=375%2C194\" alt=\"[1\/0 = infinito]\" width=\"375\" height=\"194\" class=\"aligncenter size-full wp-image-263\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf1.jpg?w=375&amp;ssl=1 375w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf1.jpg?resize=300%2C155&amp;ssl=1 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/a><br \/>\nRuotiamo ora entrambi i membri di novanta gradi in senso antiorario:<br \/>\n<a href=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf2.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"264\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2014\/05\/12\/aritmetica-con-linfinito-pillole\/inf2\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf2.jpg?fit=417%2C159&amp;ssl=1\" data-orig-size=\"417,159\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"inf2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf2.jpg?fit=417%2C159&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf2.jpg?resize=417%2C159\" alt=\"[ -10 = 8 ]\" width=\"417\" height=\"159\" class=\"aligncenter size-full wp-image-264\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf2.jpg?w=417&amp;ssl=1 417w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf2.jpg?resize=300%2C114&amp;ssl=1 300w\" sizes=\"auto, (max-width: 417px) 100vw, 417px\" \/><\/a><br \/>\nSottraiamo 8 da entrambi i membri:<br \/>\n<a href=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf3.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"265\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2014\/05\/12\/aritmetica-con-linfinito-pillole\/inf3\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf3.jpg?fit=392%2C160&amp;ssl=1\" data-orig-size=\"392,160\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"inf3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf3.jpg?fit=392%2C160&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf3.jpg?resize=392%2C160\" alt=\"[ -18 = 0 ]\" width=\"392\" height=\"160\" class=\"aligncenter size-full wp-image-265\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf3.jpg?w=392&amp;ssl=1 392w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf3.jpg?resize=300%2C122&amp;ssl=1 300w\" sizes=\"auto, (max-width: 392px) 100vw, 392px\" \/><\/a><br \/>\nRuotiamo infine entrambi i membri di novanta gradi in senso orario:<br \/>\n<a href=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf4.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"266\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2014\/05\/12\/aritmetica-con-linfinito-pillole\/inf4\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf4.jpg?fit=410%2C223&amp;ssl=1\" data-orig-size=\"410,223\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"inf4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf4.jpg?fit=410%2C223&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/05\/inf4.jpg?resize=410%2C223\" alt=\"[ 1\/infinito = 0 ]\" width=\"410\" height=\"223\" class=\"aligncenter size-full wp-image-266\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf4.jpg?w=410&amp;ssl=1 410w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2014\/05\/inf4.jpg?resize=300%2C163&amp;ssl=1 300w\" sizes=\"auto, (max-width: 410px) 100vw, 410px\" \/><\/a><br \/>\nVisto? Torna tutto!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>non \u00e8 difficile fare operazioni con l&#8217;infinito: basta disegnare bene<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_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,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[76,32],"class_list":["post-262","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-humour","tag-pillole"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/phh2yP-4e","jetpack-related-posts":[{"id":2594,"url":"https:\/\/xmau.com\/ilpost\/2013\/04\/15\/integermania-pillole\/","url_meta":{"origin":262,"position":0},"title":"Integermania [Pillole]","author":".mau.","date":"15\/04\/2013","format":false,"excerpt":"come ottenere i numeri da 1 a 100 in modi creativi","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2632,"url":"https:\/\/xmau.com\/ilpost\/2013\/09\/03\/a-game-of-numbers-pillole\/","url_meta":{"origin":262,"position":1},"title":"&#8220;A game of Numbers&#8221; [Pillole]","author":".mau.","date":"03\/09\/2013","format":false,"excerpt":"Iniziamo il cosiddetto \"anno logico\" in maniera leggera.","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2586,"url":"https:\/\/xmau.com\/ilpost\/2013\/04\/06\/citazioni-da-_the-joy-of-x_-pillole\/","url_meta":{"origin":262,"position":2},"title":"Citazioni da _The Joy of x_ [Pillole]","author":".mau.","date":"06\/04\/2013","format":false,"excerpt":"Citazioni matematiche dal libro di Steven Strogatz","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2592,"url":"https:\/\/xmau.com\/ilpost\/2013\/04\/12\/spending-review-sulle-operazioni\/","url_meta":{"origin":262,"position":3},"title":"Spending review sulle operazioni","author":".mau.","date":"12\/04\/2013","format":false,"excerpt":"Con un po' di contorsioni, e ammettendo l'esistenza a priori di 0 e 1, \u00e8 possibile definire una singola operazione dalla quale si possono ottenere le quattro usuali operazioni.","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2428,"url":"https:\/\/xmau.com\/ilpost\/2011\/08\/09\/il-paradosso-di-ross-littlewood\/","url_meta":{"origin":262,"position":4},"title":"Il paradosso di Ross-Littlewood","author":".mau.","date":"09\/08\/2011","format":false,"excerpt":"L'infinito \u00e8 una brutta bestia, su questo credo siano in molti a essere d'accordo. Ma se si immagina di compiere un numero infinito di azioni in un tempo finito, i paradossi aumentano ancora!","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":727,"url":"https:\/\/xmau.com\/ilpost\/2016\/03\/09\/la-congettura-degli-insiemi-union-closed-pillole\/","url_meta":{"origin":262,"position":5},"title":"La congettura degli insiemi union-closed [Pillole]","author":".mau.","date":"09\/03\/2016","format":false,"excerpt":"Partiamo da una definizione non molto complicata. Una famiglia di insiemi si dice chiuso rispetto all'unione (\"union-closed\" in inglese, forma che user\u00f2 perch\u00e9 molto pi\u00f9 compatta) se presi due qualunque insiemi della famiglia la loro unione fa ancora parte della famiglia. Prendiamo per esempio la famiglia formata da {}, {1,3},\u2026","rel":"","context":"In \"combinatorica\"","block_context":{"text":"combinatorica","link":"https:\/\/xmau.com\/ilpost\/tag\/combinatorica\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/262","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/comments?post=262"}],"version-history":[{"count":1,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/262\/revisions"}],"predecessor-version":[{"id":267,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/262\/revisions\/267"}],"wp:attachment":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/media?parent=262"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/categories?post=262"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/tags?post=262"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}