Lifestyle Khazanah Profil Baru Dram Lists Ensiklopedia
Technopedia Center
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Faculty of Engineering and Computer Science
S1 Informatics S1 Information Systems S1 Information Technology S1 Computer Engineering S1 Electrical Engineering S1 Civil Engineering

faculty of Economics and Business
S1 Management S1 Accountancy

Faculty of Letters and Educational Sciences
S1 English literature S1 English language education S1 Mathematics education S1 Sports Education
teknopedia

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url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url url 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url url
  2. Weltenzyklopädie
  3. میدان بسته جبری - ویکی‌پدیا، دانشنامهٔ آزاد
میدان بسته جبری - ویکی‌پدیا، دانشنامهٔ آزاد
از ویکی‌پدیا، دانشنامهٔ آزاد

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اعداد حقیقی یک میدان بسته نیست زیرا برای مثال چندجمله ایِ x۲ + ۱ = ۰ در اعداد حقیقی دارای ریشه نیست در حالیکه تمام ضرایب جملات آن حقیقی هستند و x دارای توانی بزرگتر مساوی یک می باشد. به همین ترتیب می توان گفت که هیچ زیرمیدانی از اعداد حقیقی هم میدان بسته ای نیست پس مجموعه ی اعداد گویا نیز میدان بسته ای نمی‌باشد. همچنین؛ هیچ میدان متناهیِ F نیز بسته نمی‌باشد.

اثبات: اگر اعضای F را a۱،a۲،...،an در نظر بگیریم، چندجمله‌ایِ x − a۱)(x − a۲) ··· (x − an) + ۱) دارای هیچ ریشه ای در F نمی‌باشد.

گاوس در قضیه ی اساسیِ جبر اثبات کرد که مجموعه ی اعداد مختلط یک میدان بسته است.

Pusat Layanan

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