{"id":53351,"date":"2024-02-26T15:03:00","date_gmt":"2024-02-26T14:03:00","guid":{"rendered":"https:\/\/studybuddy.se\/vad-ar-reela-tal\/"},"modified":"2026-10-16T09:29:21","modified_gmt":"2026-10-16T08:29:21","slug":"vad-ar-reella-tal","status":"publish","type":"post","link":"https:\/\/studybuddy.se\/en\/vad-ar-reella-tal\/","title":{"rendered":"Vad \u00e4r reella tal?"},"content":{"rendered":"<h2><b>Olika talm\u00e4ngder<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Tal kan delas in i olika talm\u00e4ngder. P\u00e5 gymnasiet arbetar man framf\u00f6r allt med reella tal, men i de h\u00f6gre matematikkurserna ing\u00e5r \u00e4ven komplexa tal. Reella tal innefattar alla tal som kan placeras ut p\u00e5 tallinjen, till skillnad fr\u00e5n komplexa tal, som inte kan det.<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-24842\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy.jpg\" alt=\"reela-tal-studybuddy\" width=\"495\" height=\"104\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy.jpg 1860w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-300x63.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-1024x215.jpg 1024w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-768x161.jpg 768w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-1536x322.jpg 1536w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-1280x268.jpg 1280w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reela-tal-studybuddy-1000x210.jpg 1000w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">De reella talen har emellertid flera delm\u00e4ngder, n\u00e4mligen rationella tal, heltal, och naturliga tal. Olika delm\u00e4ngder ing\u00e5r f\u00f6r \u00f6vrigt i varandra, som bilden nedanf\u00f6r visar.<\/span><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-24843\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy.jpg\" alt=\"Reela-tal-studybuddy\" width=\"599\" height=\"178\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy.jpg 1902w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-300x89.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-1024x305.jpg 1024w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-768x229.jpg 768w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-1536x457.jpg 1536w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-1280x381.jpg 1280w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-2-studybuddy-1000x298.jpg 1000w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<h3><b>Naturliga tal<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">De naturliga talen innefattar alla positiva heltal, inklusive noll. De brukar betecknas med bokstaven N.<\/span><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-24844\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-3-studybuddy.jpg\" alt=\"Reela-tal-studybuddy\" width=\"308\" height=\"91\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-3-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-3-studybuddy-300x89.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-3-studybuddy-768x227.jpg 768w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<h3><b>Heltal<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Heltalen \u00e4r helt enkelt alla heltal, b\u00e5de negativa och positiva. De naturliga talen ing\u00e5r allts\u00e5 i gruppen heltal. Heltalen betecknas med Z.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-24846\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-4-studybuddy.jpg\" alt=\"Reela-tal-studybuddy\" width=\"413\" height=\"88\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-4-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-4-studybuddy-300x64.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/Reela-tal-4-studybuddy-768x164.jpg 768w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<h3><b>Rationella tal<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Alla tal som kan uttryckas som ett br\u00e5k d\u00e4r n\u00e4mnaren och t\u00e4ljaren \u00e4r heltal \u00e4r rationella tal. De kan allts\u00e5 vara positiva eller negativa, heltal eller decimaltal. N\u00e4mnaren kan f\u00f6rst\u00e5s inte vara noll! Rationella tal betecknas med Q.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Reella tal<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Som tidigare n\u00e4mnt \u00e4r de reella talen samtliga tal som kan placeras p\u00e5 tallinjen. Denna grupp inkluderar allts\u00e5 rationella tal, heltal, och naturliga tal. Ut\u00f6ver dessa grupper finns n\u00e5gra tal som inte kan uttryckas som ett br\u00e5k med heltal, och allts\u00e5 inte r\u00e4knas som rationella tal. Ett exempel p\u00e5 ett s\u00e5dant tal \u00e4r pi, .<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Komplexa tal<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Tal som inte kan placeras p\u00e5 tallinjen kallas f\u00f6r komplexa tal, och har en imagin\u00e4r del. Ett exempel p\u00e5 imagin\u00e4ra tal \u00e4r <\/span><i><span style=\"font-weight: 400;\">i<\/span><\/i><span style=\"font-weight: 400;\">, som \u00e4r roten ur -1. Komplexa tal kan ha b\u00e5de imagin\u00e4ra och reella del, exempelvis <\/span><span style=\"font-weight: 400;\">2 + 4i<\/span><span style=\"font-weight: 400;\">, d\u00e4r 2 \u00e4r den rationella delen och 4<\/span><i><span style=\"font-weight: 400;\">i<\/span><\/i><span style=\"font-weight: 400;\"> \u00e4r den imagin\u00e4ra delen. Tal som enbart har imagin\u00e4ra delar kallas rent imagin\u00e4ra. <\/span><span style=\"font-weight: 400;\">2i<\/span><span style=\"font-weight: 400;\"> \u00e4r ett exempel p\u00e5 ett rent imagin\u00e4rt tal.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Reella och komplexa r\u00f6tter<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Andragradsekvationer kan ha tv\u00e5, en, eller noll reella r\u00f6tter. Om en andragradsekvation endast har en reell rot kallas det f\u00f6r en reell dubbelrot. <a href=\"http:\/\/studybuddy.se\/en\/vad-ar-pq-formeln\/\">PQ-formeln<\/a> kan anv\u00e4ndas f\u00f6r att avg\u00f6ra hur m\u00e5nga reella r\u00f6tter en andragradsekvation har.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-24853\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-studybuddy.jpg\" alt=\"pq-formeln-studybuddy\" width=\"506\" height=\"44\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-studybuddy-300x26.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-studybuddy-768x67.jpg 768w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-24854\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-2-studybuddy.jpg\" alt=\"pq-formeln-studybuddy\" width=\"672\" height=\"82\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-2-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-2-studybuddy-300x37.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/pq-formeln-2-studybuddy-768x94.jpg 768w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Om diskriminanten \u00e4r positiv finns det tv\u00e5 reella r\u00f6tter, \u00e4r diskriminanten noll finns det en reell rot, och \u00e4r diskriminanten negativ finns det inga reella r\u00f6tter.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h4><strong>Nedan f\u00f6ljer n\u00e5gra exempel:<\/strong><\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-24857\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-1-studybuddy.jpg\" alt=\"reel-rot-studybuddy\" width=\"627\" height=\"227\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-1-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-1-studybuddy-300x109.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-1-studybuddy-768x278.jpg 768w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-24858\" src=\"http:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-2-studybuddy.jpg\" alt=\"reel-rot-studybuddy\" width=\"625\" height=\"191\" srcset=\"https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-2-studybuddy.jpg 1000w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-2-studybuddy-300x92.jpg 300w, https:\/\/studybuddy.se\/wp-content\/uploads\/2024\/02\/reel-rot-2-studybuddy-768x235.jpg 768w\" sizes=\"(max-width: 625px) 100vw, 625px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Tveka inte att h\u00f6ra av dig om du vill ha hj\u00e4lp med <a href=\"http:\/\/studybuddy.se\/en\/\">l\u00e4xhj\u00e4lp<\/a>.<\/p>","protected":false},"excerpt":{"rendered":"<p>Olika talm\u00e4ngder Tal kan delas in i olika talm\u00e4ngder. P\u00e5 gymnasiet arbetar man framf\u00f6r allt med reella tal, men i de h\u00f6gre matematikkurserna ing\u00e5r \u00e4ven komplexa tal. Reella tal innefattar alla tal som kan placeras ut p\u00e5 tallinjen, till skillnad fr\u00e5n komplexa tal, som inte kan det. De reella talen har emellertid flera delm\u00e4ngder, n\u00e4mligen [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":24861,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2006],"tags":[],"class_list":["post-53351","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-guide-studiehjalp"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.3 (Yoast SEO v28.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Vad \u00e4r reella tal? | Studybuddy L\u00e4xhj\u00e4lp<\/title>\n<meta name=\"description\" content=\"Vad \u00e4r reella tal? L\u00e4r dig talm\u00e4ngderna, naturliga tal, heltal, rationella och reella tal. 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