institute 发表于 2025-3-25 07:21:06

Introduction Foundations Research,r, there are many numbers that are not algebraic over .. In fact, the algebraically closed field of all algebraic numbers in . is a countable set, for you can check that the algebraic numbers over . that have a minimal polynomial of degree . are countable. Letting . vary gives a countable collection of countable sets, which is therefore countable.

CRAMP 发表于 2025-3-25 10:35:50

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抚育 发表于 2025-3-25 13:02:14

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Fecundity 发表于 2025-3-25 18:19:15

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SLUMP 发表于 2025-3-25 21:46:44

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FAWN 发表于 2025-3-26 02:54:12

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媒介 发表于 2025-3-26 05:00:20

Dialing In Problems,ndem with) your formal instruction or reading. They cover a wide range of topics. Some of them will not be familiar to you. But try them now, look things up (in this book, for example), and come back to them as you proceed through the text.

冰河期 发表于 2025-3-26 09:05:58

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BAIL 发表于 2025-3-26 13:59:25

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潜移默化 发表于 2025-3-26 20:29:44

Irrational, Algebraic, and Transcendental Numbers,r, there are many numbers that are not algebraic over .. In fact, the algebraically closed field of all algebraic numbers in . is a countable set, for you can check that the algebraic numbers over . that have a minimal polynomial of degree . are countable. Letting . vary gives a countable collection
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查看完整版本: Titlebook: Excursions in Number Theory, Algebra, and Analysis; Kenneth Ireland,Al Cuoco Textbook 2023 The Editor(s) (if applicable) and The Author(s)