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Öğretmen, Ferhat, Merve, Yağmur ve İbrahim gibi öğrencilerin de katıldığı bir ders ortamında sunum yapmaktadır.","Videoda köklü sayılar konusu detaylı bir şekilde ele alınmaktadır. Öğretmen, köklü ifadelerin özellikleri, kök dışına çıkarma kuralları, köklü sayıların üslü sayı şeklinde yazımı, kök derecelerinin genişletilmesi/sadeleştirilmesi, köklü ifadelerde toplama-çıkarma-çarpma-bölme işlemlerinin nasıl yapılacağı, köklü sayıların eşlenikleri ve kök içinde muhabbetler konularını örneklerle açıklamaktadır.","Video, 2. dönem sonu soru çözümlerini içeren interaktif bir ders formatında ilerlemektedir. Öğretmen, hastalıktan dolayı yorulduğunu belirterek izleyicilere özür dilerken, konuyu adım adım ve pratik örneklerle anlatmaktadır. Video, bir soru çözümüyle ve ödüllü bir soruyla sona ermektedir."]},"endTime":3073,"title":"9. Sınıf Köklü Sayılar Canlı Yayın Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"9. 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olmalıdır.","Köklü ifadelerde payda sıfır olamaz, bu da çözüme etki edebilir."]},"beginTime":279,"endTime":554,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=279&ask_summarization=1"},{"index":4,"title":"Köklü İfadelerin Özelliklerinin Uygulanması","list":{"type":"unordered","items":["Köklü ifadelerde kök dışına çıkarma işlemi yapılırken, kökün derecesi ile üstün derecesi aynıysa birbirini götürür ve içteki ifade dışarı çıkar.","Tek dereceli köklü ifadelerde içteki ifade direkt dışarı çıkar, çift dereceli köklü ifadelerde ise mutlak değer dışarı çıkar.","Çift dereceli köklü ifadelerde mutlak değer dışarı çıkarıldığından, sonucun her zaman pozitif olması 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Yazma","list":{"type":"unordered","items":["Matematikte önemli olan bir kuralı bilmek değil, düzgün yazmak ve tersten okumaktır.","Tersten okuma, nasıl dışarı çıktığını düşünerek içeriye yerleştirme işlemidir (örneğin, a üzeri en dışarı çıkıyorsa, içeriye a üzeri en olarak girer).","Kök içindeki sayıları kare, küp veya diğer kuvvetler olarak yazarak dışarı çıkarma işlemi yapılabilir (örneğin: 18 = 9×2, 72 = 36×2)."]},"beginTime":886,"endTime":1142,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=886&ask_summarization=1"},{"index":7,"title":"Köklü Sayıların Üslü Sayı Şeklinde Yazımı","list":{"type":"unordered","items":["Her köklü sayı aynı zamanda bir üslü sayıdır.","Kök işaretinin üst üste yazılması, üslü sayı şeklinde yazımın temelidir (örneğin: ³√252 = 252^(1/3)).","Üslü sayı şeklinde yazım, tabanlar aynıysa üstlerin toplanması veya çıkarılması gibi işlemlerde kolaylık sağlar."]},"beginTime":1142,"endTime":1378,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1142&ask_summarization=1"},{"index":8,"title":"Kök Derecelerinin Genişletilmesi ve Sadeleştirilmesi","list":{"type":"unordered","items":["Kök derecesi genişletilebilir veya sadeleştirilebilir, ancak içeriğin de aynı şekilde genişletilmesi veya sadeleştirilmesi gerekir.","Kök derecelerinin eşitlenmesi, sıralama sorularında ve iç içe köklerde kullanışlıdır.","Kök içindeki üst 1 ve kök derecesi 2 olduğunda, bunlar yazılmaz (örneğin: √a = a^(1/2))."]},"beginTime":1378,"endTime":1501,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1378&ask_summarization=1"},{"index":9,"title":"Sıralama Sorularında Kök Derecelerinin Eşitlenmesi","list":{"type":"unordered","items":["Sıralama sorularında, köklerin tabanları eşitlenir veya dereceleri eşitlenir.","Kök derecelerini eşitlemek için, her kökün derecesini aynı sayıya genişletmek gerekir (örneğin: ²√a, ³√b, ⁴√c'yi ¹²√a, ¹²√b, ¹²√c şeklinde eşitlemek).","Dereceleri eşitlendikten sonra, kök içindeki sayılar karşılaştırılarak sıralama yapılır."]},"beginTime":1501,"endTime":1587,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1501&ask_summarization=1"},{"index":10,"title":"Köklü İfadelerde Toplama ve Çıkarma","list":{"type":"unordered","items":["Köklü ifadelerde toplama ve çıkarma işlemi yapılırken, kök kuvveti ve içi aynı olan terimler toplanıp çıkarılır.","Kök kuvveti veya içi farklı olan terimler toplanamaz veya çıkarılamaz.","Köklü ifadelerde toplama ve çıkarma işlemi, üslü sayılarda olduğu gibi aynı terimlerin toplanması gibidir."]},"beginTime":1592,"endTime":1889,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1592&ask_summarization=1"},{"index":11,"title":"Köklü İfadelerde Çarpma ve Bölme","list":{"type":"unordered","items":["Kök kuvvetleri aynı olan köklü ifadeler çarpılır veya bölünürken, kök içine girerler ve çarpılırlar.","Kök kuvvetleri farklı olan ifadeler çarpılırken önce kök kuvvetleri eşitlenir.","Kök kuvvetlerini eşitlemek için, kökün derecesi ile genişletme yapılır ve içteki sayılar da aynı oranda çarpılır."]},"beginTime":1889,"endTime":2065,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1889&ask_summarization=1"},{"index":12,"title":"Eşlilik Kavramı","list":{"type":"unordered","items":["Eşlilik kavramı, köklü ifadeleri kökten kurtarmak için kullanılır.","Köklü ifadeleri eşliliği ile çarptığımızda, iki kare farkı formülü kullanılarak kökten kurtulur.","Bir köklü ifadenin eşlisi, kök içindeki ifadenin işaretini değiştirerek bulunur (örneğin, kök x - kök y'nin eşlisi kök x + kök y'dir)."]},"beginTime":2065,"endTime":2248,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2065&ask_summarization=1"},{"index":13,"title":"Köklü Sayıların Eşleniği","list":{"type":"unordered","items":["Köklü sayıların kökten kurtarılması için eşlenik çarpımı yapılır.","Kök beş eksi kök üç ile kök beş artı kök üç çarpıldığında, kökler birbirini götürüp sayılar kalır.","Köklü sayıların eşlenik çarpımı a²-b² formülüne göre hesaplanır."]},"beginTime":2252,"endTime":2307,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2252&ask_summarization=1"},{"index":14,"title":"Köklü Sayıların Çarpımı","list":{"type":"unordered","items":["Köklü sayıların çarpımı a²-b² formülüne göre hesaplanır.","Köklerin karesi alınarak sonuç bulunur.","Köklü sayıların çarpımında genellikle terimler birbirini götürür."]},"beginTime":2307,"endTime":2384,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2307&ask_summarization=1"},{"index":15,"title":"Köklü Sayıların Kökten Kurtarılması","list":{"type":"unordered","items":["Köklü sayıların kökten kurtarılması için eşlenik çarpımı yapılır.","Pay ve payda eşlenikle çarpılır, kökler birbirini götürür.","Sonuçta köklü sayılar sadeleştirilir."]},"beginTime":2384,"endTime":2465,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2384&ask_summarization=1"},{"index":16,"title":"Kök İçinde Muhabbetler","list":{"type":"unordered","items":["Kök içinde muhabbetler üslü sayılara benzer şekilde işlem yapılır.","Kök kök içinde sayı yoksa, dereceler çarpılarak tek kök içinde ifade edilir.","Kök kök içinde sayı varsa, içeri girerken üs alınarak işlem yapılır."]},"beginTime":2465,"endTime":2655,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2465&ask_summarization=1"},{"index":17,"title":"Kök İçinde Muhabbet Örnekleri","list":{"type":"unordered","items":["Kök içinde muhabbetlerde dışarıdaki kökler içeri girerken üs alınır.","Dereceler çarpılarak tek kök içinde ifade edilir.","Kök içindeki sayılar çarpılarak tek kök içinde ifade edilir."]},"beginTime":2655,"endTime":2801,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2655&ask_summarization=1"},{"index":18,"title":"Köklü Sayıların Kareleri","list":{"type":"unordered","items":["(a+b)² formülü hatırlatılıyor: birinci terimin karesi, iki terimin çarpımının iki katı ve ikinci terimin karesi toplamı.","Örnek olarak (√3+√2)² hesaplanıyor: 3+2√6+2=5+2√6.","İki köklü sayının karesi alınırken, sonuç iki sayının toplamı ve çarpımı şeklinde ifade edilir."]},"beginTime":2803,"endTime":2899,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2803&ask_summarization=1"},{"index":19,"title":"Köklü Sayıların Çözümü","list":{"type":"unordered","items":["x=iki sayının toplamı ve y=iki sayının çarpımı şeklindeki ifadelerde, kök içindeki ifade köklü sayıların karesi olarak yazılabilir.","İşlemdeki \"2\" terimi çok önemlidir, bu terim görünce çözümü tamamlamak mümkündür.","Örnek olarak 5+2√6 ifadesi √3-√2 şeklinde yazılabilir."]},"beginTime":2899,"endTime":2983,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2899&ask_summarization=1"},{"index":20,"title":"Örnek Sorular","list":{"type":"unordered","items":["İzleyicilere 11+2√18 ifadesini çözmeleri isteniyor.","Çözüm: 9+2=11 ve 9×2=18 olduğundan, ifade √9+√2 şeklinde yazılır.","Köklü sayılar canlı yayını burada sona eriyor ve izleyicilerden cevaplarını yorumlara bırakmaları isteniyor."]},"beginTime":2983,"endTime":3053,"href":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2983&ask_summarization=1"}],"linkTemplate":"/video/preview/8895756362113893670?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"9. 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Öğretmen, \"Yer ve Zaman\" ünitesinin bir parçası olan coğrafi koordinat sistemi konusunu anlatmaktadır.","Video, coğrafi koordinat sisteminin temel kavramlarını sistematik olarak ele almaktadır. İlk olarak kutup ve ekvator kavramları, paraleller ve meridyenler tanıtılmakta, ardından enlem kavramı ve enlem etkisi detaylı şekilde açıklanmaktadır. Daha sonra meridyenler, yerel saat, saat dilimleri, Greenwich meridyeni, tarih değiştirme çizgisi ve anti-meridyen kavramları anlatılmaktadır.","Videoda kitaptan 36-38. sayfaları kapsamakta ve konular görsel örneklerle desteklenmektedir. Ayrıca, enlem etkisinin bitki örtüsü, denizlerin tuzluluğu, basınç alanları ve sıcaklık gibi konulardaki etkileri örneklerle açıklanmakta, yerel saat hesaplamaları ve zaman farkı hesaplamaları örneklerle pekiştirilmektedir. Video, öğrencilere ödevlendirme ve ödüllü soru ile sonlanmaktadır."]},"endTime":1850,"title":"Coğrafi Koordinat Sistemi ve Saat Dilimleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Coğrafi Koordinat Sistemi Konusuna Giriş","list":{"type":"unordered","items":["Uzaktan eğitimle coğrafi koordinat sistemi konusu işlenecek.","Ünite içeriğinde yer ve zaman, paralel enlem, meridyen, boylam ve yerel saat kavramları ele alınacak.","Bir sonraki derste yer ve zaman ünitesi tamamlanacak, Türkiye'nin coğrafi konumu öğrenilecek."]},"beginTime":1,"endTime":101,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1&ask_summarization=1"},{"index":1,"title":"Koordinat Sisteminin Temel Kavramları","list":{"type":"unordered","items":["Koordinat sistemi, dünya üzerindeki herhangi bir yerin konumunu ve zaman-yere ait özelliklerini belirlemek için oluşturulmuştur.","Kutup, dünyanın kendi ekseni etrafındaki hareketi sırasında dönmeyen hareketsiz noktalardır; 90 derece kuzey enlemi kuzey kutup noktasını, 90 derece güney enlemi ise güney kutup noktasını oluşturur.","Ekvator, dünyayı kuzey ve güney olmak üzere iki eşit kısma ayıran, doğu-batı yönlü uzanan en geniş paralel dairesidir ve 0 derece enlemdir."]},"beginTime":101,"endTime":168,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=101&ask_summarization=1"},{"index":2,"title":"Paralellerin Özellikleri","list":{"type":"unordered","items":["Paraleller, ekvatora bir derece aralıklarla çizilen dairelerdir ve toplam 180 tane paralel dairesi bulunmaktadır.","Ekvatorun kuzeyinde çizebileceğimiz toplam 90 tane, güneyinde de çizebileceğimiz 90 tane paralel dairesi vardır.","Paraleller hiçbir zaman birbirlerini kesmezler, aralarındaki kuş uçuşu mesafe sabittir ve 111 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başlangıç paraleline olan uzaklığının açı cinsinden ifadesine enlem denir.","Enlem, derece, dakika ve saniye cinsinden ifade edilir; örneğin Ankara'nın enlemi 39 derece 57 dakika kuzey enlemidir.","Her paralel derecesi bir enlemdir ama her enlem bir paralel değildir."]},"beginTime":555,"endTime":641,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=555&ask_summarization=1"},{"index":5,"title":"Enlem Etkisi","list":{"type":"unordered","items":["Enlem etkisi, ekvatordan kutuplara doğru gidildikçe meydana gelen değişimlerdir ve güneş ışınlarının geliş açısına bağlıdır.","Güneş ışınlarının geliş açısı ekvatordan kutuplara doğru gidildikçe daralır, bu nedenle cisimlerin gölge boyları uzar.","Sıcaklık değerleri, deniz ve okyanuslardaki buharlaşma miktarı, tuzluluk oranı ve kalıcı kar alt sınırı ekvatordan kutuplara doğru gidildikçe azalır."]},"beginTime":641,"endTime":765,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=641&ask_summarization=1"},{"index":6,"title":"Bitki Örtüsü ve Ekonomik Etkinlikler","list":{"type":"unordered","items":["Bitki örtüsü kuşaklar oluşturur: ekvator çevresinde geniş yapraklı ormanlar, orta kuşak çevresinde karma yapraklı ormanlar, kutup altı alanlarında iğne yapraklı ormanlar ve tundralar bulunur.","Ekvatordan kutuplara doğru gidildikçe ekonomik etkinlikler ve faaliyetler değişir."]},"beginTime":765,"endTime":789,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=765&ask_summarization=1"},{"index":7,"title":"Enlem Etkisi","list":{"type":"unordered","items":["Enlem etkisiyle açıklanabilir durumlar: Brezilya'da geniş yapraklı ağaçlar, Umman Denizi'nin Baltık Denizinden daha tuzlu olması, Kongo Havzasında termik alçak basınç görülmesi.","Enlem etkisine ters düşen durumlar: Londra'nın Ottova'dan sıcak olması, Ocak ayında Avustralya'nın ekvatordan daha sıcak olması, Sibirya'nın kuzey kutbundan soğuk olması.","Enlem etkisiyle açıklanabilir durumlar: Arabistan'da daimi kar sınırının Kanada'dan yüksek olması, Grönland'da yerçekiminin Türkiye'den fazla olması, Türkiye'de güneş ışınlarının tutulma oranının Endonezya'dan fazla olması."]},"beginTime":793,"endTime":1004,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=793&ask_summarization=1"},{"index":8,"title":"Meridyenler","list":{"type":"unordered","items":["Meridyen, iki kutup noktası arasında uzanan paralel dairelerin dik kesen hayali yarım dairelerdir ve başlangıç meridyeni İngiltere'nin Greenge kasabasından geçer.","Meridyenler paraleller gibi bir derece aralıklarla çizilmiştir ve aynı sayısal değerden iki tane olduğu için yön belirtilmelidir.","Başlangıç meridyenin sol tarafında batı yarım küre, sağ tarafında doğu yarım küre bulunur ve her yarım kürede toplam 180 meridyen yayı vardır."]},"beginTime":1004,"endTime":1096,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1004&ask_summarization=1"},{"index":9,"title":"Meridyenlerin Özellikleri","list":{"type":"unordered","items":["Aynı meridyen üzerindeki bütün noktaların yerel saatleri aynıdır ve tüm meridyenlerin uzunlukları birbirine eşittir.","Ardışık iki meridyen arasındaki yerel saat farkı dört dakikadır çünkü dünya kendi ekseni etrafındaki bir tam turunu 24 saatlik sürede tamamlar ve 360 meridyeni geçer.","Dünya üzerindeki herhangi bir yerin başlangıç meridyeni uzaklığının açı cinsinden değeridir ve Ankara 32 derece 53 dakika 15 saniye doğu boylamında yer alır."]},"beginTime":1096,"endTime":1198,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1096&ask_summarization=1"},{"index":10,"title":"Yerel Saat","list":{"type":"unordered","items":["Yerel saat, güneşin ufuk düzlemindeki konumuna göre belirlenen zaman kavramıdır ve namaz vakitleri, iftar ve sahur vakitleri yerel saate göre belirlenir.","Her bir derecelik boylam arasındaki zaman farkı dört dakikadır ve aynı boylam üzerindeki tüm noktalarda yerel saat aynıdır.","Bir boylamın tam karşısında yerel saat 12'dir (öğle vakti), bir boylamın daha doğusunda yerel saat ileri, daha batısında ise yerel saat geridir."]},"beginTime":1198,"endTime":1280,"href":"/video/preview/7288770454586455661?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1198&ask_summarization=1"},{"index":11,"title":"Saat Dilimleri ve Ortak Saat 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Öğretmen, konuyu adım adım ve çeşitli örneklerle açıklamaktadır.","Video, kümeler konusunu beş ana bölüme ayrılmış olarak ele almaktadır: kümelere giriş, kümelerin gösterim yöntemleri (liste, şema ve ortak özellik), kümelerin türleri (boş küme, sonlu küme, sonsuz küme, evrensel küme), eşit kümeler ve alt küme kavramları. Her bölümde teorik bilgiler verildikten sonra günlük hayattan örneklerle ve Venn şemaları kullanılarak konu pekiştirilmektedir.","Video ayrıca alt küme sayısı hesaplama yöntemleri (2 üzeri eleman sayısı), özalt küme kavramı ve yazılı sınavlara hazırlık amacıyla örnek sorular çözümü içermektedir. Öğretmen, kavramları hem teorik hem de pratik olarak anlatarak, öğrencilerin konuyu daha iyi anlamalarını sağlamaktadır."]},"endTime":3190,"title":"Kümeler Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Kümelerin Tanımı","list":{"type":"unordered","items":["Kümeler konusu üç bölüme ayrılmıştır: kümelere giriş, kümelerin özellikleri ve kümelerin gösterimi.","İyi tanımlanmış birbirinden farklı nesneler topluluğuna küme denir.","Kümeyi oluşturan nesnelerin her birine kümenin elemanı denir."]},"beginTime":4,"endTime":53,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=4&ask_summarization=1"},{"index":1,"title":"Küme Örnekleri","list":{"type":"unordered","items":["\"Altıdan küçük rakamlar\" bir kümedir çünkü iyi tanımlanmış ve elemanları net bir şekilde anlaşılmaktadır.","\"Sonbahar mevsiminin ayları\" (Eylül, Ekim, Kasım) bir kümedir çünkü iyi tanımlanmış ve elemanları farklıdır.","\"Bazı günler\" bir küme değildir çünkü iyi tanımlanmamıştır.","\"İki basamaklı tam sayılar\" bir kümedir çünkü iyi tanımlanmış ve elemanları farklıdır.","\"Güzel filmler\" bir küme değildir çünkü kişisel değerlendirmelere dayanır ve iyi tanımlanmamıştır."]},"beginTime":53,"endTime":185,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=53&ask_summarization=1"},{"index":2,"title":"Kümelerin Özellikleri","list":{"type":"unordered","items":["Kümeler genellikle büyük harfle gösterilir (A kümesi, B kümesi, C kümesi).","Kümenin elemanları genellikle küçük harflerle gösterilir (a, b, c).","Kümede her bir eleman yalnız bir kez yazılır.","A kümesinin eleman sayısı |A| şeklinde gösterilir.","a elemanı A kümesindeyse a ∈ A şeklinde gösterilir, değilse a ∉ A şeklinde gösterilir."]},"beginTime":185,"endTime":310,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=185&ask_summarization=1"},{"index":3,"title":"Kümelerin Gösterim Yöntemleri","list":{"type":"unordered","items":["Kümelerin gösteriminde üç farklı yöntem bulunmaktadır: liste yöntemi, şeması yöntemi ve ortak özellik yöntemi.","Liste yöntemi, kümeye ait elemanların süslü parantez içinde virgülle ayrılarak yazılmasıyla gerçekleştirilir.","Kümeler genellikle büyük harflerle gösterilir ve liste yönteminde virgülle ayrılan her bir eleman kümenin bir elemanıdır."]},"beginTime":316,"endTime":370,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=316&ask_summarization=1"},{"index":4,"title":"Liste Yöntemi Örnekleri","list":{"type":"unordered","items":["Çift rakamlar kümesi liste yöntemiyle {0, 2, 4, 6, 8} şeklinde gösterilir.","\"Ankaralılar\" kelimesinin harflerini liste yöntemiyle gösterirken, her harf yalnızca bir kez yazılır ve kümenin eleman sayısı 5'tir.","Kümelerin eleman sayısı, kümenin içindeki farklı elemanların sayısını ifade eder."]},"beginTime":370,"endTime":536,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=370&ask_summarization=1"},{"index":5,"title":"Şeması Yöntemi","list":{"type":"unordered","items":["Şeması yöntemi, kümenin elemanlarının kapalı bir şeklin içerisinde her bir eleman için nokta koyarak gösterilmesidir.","Kapalı şekil yuvarlak, üçgen veya kare şeklinde olabilir ve her elemanın önüne bir nokta konulur.","Asal rakamlar kümesi şeması yöntemiyle gösterildiğinde, 2, 3, 5 ve 7 rakamlarının önüne nokta konulur."]},"beginTime":536,"endTime":643,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=536&ask_summarization=1"},{"index":6,"title":"Ortak Özellik Yöntemi","list":{"type":"unordered","items":["Ortak özellik yöntemi, kümedeki her elemanın sağladığı ortak özellik yazarak yapılan gösterimdir.","Bu yöntem, çok sayıda eleman içeren kümeleri kısa ve anlaşılır bir şekilde ifade etmek için kullanılır.","Ortak özellik yönteminde \"öyle ki\" sembolü (|) kullanılır ve örneğin A kümesi x | x çift rakamlar şeklinde gösterilir."]},"beginTime":643,"endTime":860,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=643&ask_summarization=1"},{"index":7,"title":"Kümelerin Listeleme Yöntemi","list":{"type":"unordered","items":["B kümesi, x'in karesi 10'dan küçük ve x tam sayı olacak şekilde tanımlanmıştır.","B kümesinin elemanları: -3, -2, -1, 0, 1, 2, 3 olup, toplam 7 elemanı vardır.","C kümesi, x = 5k şeklinde tanımlanmış olup, -20 ile 20 arasında 5'in katlarıdır."]},"beginTime":865,"endTime":1167,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=865&ask_summarization=1"},{"index":8,"title":"Küme Çeşitleri","list":{"type":"unordered","items":["Boş küme, hiç elemanı olmayan kümeyi ifade eder ve süslü parantez içinde boşlukla veya Venn şemasında yuvarlak üzerinde çizikle gösterilir.","Sonlu küme, sonlu sayıda elemana sahip olan kümeyi ifade eder.","Sonsuz küme, sonlu sayıda elemana sahip olmayan kümeyi ifade eder."]},"beginTime":1167,"endTime":1407,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1167&ask_summarization=1"},{"index":9,"title":"Sonlu ve Sonsuz Kümeler","list":{"type":"unordered","items":["Bir yılın 12 ayları sonlu sayıda ve sayılabilecek elemanlar içerdiği için sonlu kümedir.","1 ile 2 arasındaki reel sayılar sonsuz tane olduğundan, bu küme sonsuz kümedir.","5'ten küçük tam sayılar kümesi de sonsuz kümedir çünkü negatif sonsuza kadar gider.","İki basamaklı asal sayılar kümesi sonlu kümedir çünkü sayılabilecek sınırlı bir eleman sayısına sahiptir."]},"beginTime":1409,"endTime":1582,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1409&ask_summarization=1"},{"index":10,"title":"Evrensel Küme","list":{"type":"unordered","items":["Evrensel küme, üzerinde işlem yapılan tüm kümelere ait elemanları içinde bulunduran, bütün kümeleri içinde bulunduran en büyük kümedir.","Evrensel küme \"E\" ile gösterilir ve örnek olarak bir okulun sınıflarını içine alan evrensel küme olarak düşünülebilir.","Rakamlar kümesi (0-9) evrensel küme olarak gösterilirken, çift rakamlar kümesi (2, 4, 6, 8) ve tek rakamlar kümesi (5, 7, 9) evrensel kümenin alt kümeleridir."]},"beginTime":1582,"endTime":1778,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1582&ask_summarization=1"},{"index":11,"title":"Eşit Kümeler","list":{"type":"unordered","items":["Elemanları aynı olan kümelere eşit kümeler denir, eleman sayıları değil elemanların kendisinin aynı olması gerekir.","Eşit kümeler için \"=\" işareti kullanılır, örneğin A kümesi B kümesine eşitse A=B şeklinde gösterilir.","Eleman sayıları aynı olursa denk kümeler denir, ancak eşit olması için elemanların hepsinin aynı olması gerekir."]},"beginTime":1778,"endTime":1890,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1778&ask_summarization=1"},{"index":12,"title":"Alt Küme","list":{"type":"unordered","items":["A ve B gibi iki kümeden A'nın her elemanı B'nin elemanı ise A alt kümesidir B veya B kapsar A şeklinde ifade edilir.","Alt küme gösterimi \"⊆\" işaretiyle yapılır ve alt küme altta kalır, büyük küme üstte kalır.","Bir kümenin tüm elemanları başka bir kümenin içinde varsa, ilk küme ikinci kümenin alt kümesidir."]},"beginTime":1890,"endTime":2073,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=1890&ask_summarization=1"},{"index":13,"title":"Küme Özellikleri","list":{"type":"unordered","items":["Her küme kendisinin alt kümesidir çünkü tüm elemanları kendisinde bulunmaktadır.","Boş küme her kümenin alt kümesidir.","Eğer A kümesi B'nin alt kümesi ve B kümesi C'nin alt kümesiyse, otomatik olarak A kümesi C'nin alt kümesidir."]},"beginTime":2076,"endTime":2169,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2076&ask_summarization=1"},{"index":14,"title":"Alt Küme Sayısı Hesaplama","list":{"type":"unordered","items":["En elemanlı bir kümenin alt kümelerinin sayısı iki üzeri eleman sayısı şeklinde hesaplanır.","Örneğin, 2 elemanlı bir kümenin 4 alt kümesi, 4 elemanlı bir kümenin 16 alt kümesi vardır."]},"beginTime":2169,"endTime":2212,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2169&ask_summarization=1"},{"index":15,"title":"Alt Küme Örneği","list":{"type":"unordered","items":["Bir kümenin alt kümeleri, o kümenin elemanlarını ayrı ayrı yazarak (birli, ikili, üçlü) oluşturulabilir.","Boş küme her kümenin alt kümesidir.","Bir kümenin elemanları, o kümenin alt 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belirlenmelidir."]},"beginTime":2400,"endTime":2584,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2400&ask_summarization=1"},{"index":18,"title":"Özalt Küme","list":{"type":"unordered","items":["Özalt küme, bir kümenin kendisi hariç bütün alt kümeleridir."]},"beginTime":2584,"endTime":2602,"href":"/video/preview/5987625672042043636?parent-reqid=1769307501188307-5378636372049457421-balancer-l7leveler-kubr-yp-sas-251-BAL&text=kittyex9&t=2584&ask_summarization=1"},{"index":19,"title":"Alt Küme ve Özalt Küme Sayısı","list":{"type":"unordered","items":["Bir kümenin alt küme sayısı 2 üzeri n, özalt küme sayısı ise 2 üzeri n-1 ile hesaplanır.","A kümesinin alt kümesi ile özalt küme sayısı toplamı 15 olduğuna göre, A kümesinin eleman sayısı 3'tür.","Eleman sayısı 3 olan bir kümenin eleman sayısı 3 arttırılırsa, alt küme sayısı 8'e 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