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| Index
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| Preface
․
․
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| Mathematical Logic
ꊱ
ꊲ
ꊳ
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ꊱ
ꊲ
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․
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| Statements and their Connectives
ꊱ
ꊲ
ꊳ
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| Deductive Reasoning
ꊱ
ꊲ
ꊳ
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・
・
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ꊱ
ꊲ
ꊳ
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ꊱ
ꊲ
ꊱ ꊲ
ꊲ ꊲ
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⋅⋅⋅
⋅ ⋅ ⋅
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| Quantification Rules
ꊱ
ꊲ
ꊳ ꊱ
ꊲ
ꊴ
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는 로 나누어 떨어진다
는 로 나누어 떨어진다
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| Sets and their Operations
ꊱ
ꊲ
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ℕ
ℕ 은 자연수
는 의배수
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ℝ ℝ
ℕ
ℕ
ℕ
ℕ
ℕ
ℕ
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는 자연수
ℝ
ℕ
ℕ
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| Relations and Partitions
옥선 노래 보람 농구 세환 여행 소라음악듣기
ꊱ
ꊲ
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ℕ
ℝ
ℝ
―
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이하의 자연수
이하의 자연수
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∘
∘
∘ ∘
∘
ℕ
는 의 배이다 는 의 배수이다
∘
∘ 는 의 배수이다
∘ ∘ ∘ ∘
∘ ∘
∘ ∘
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∘
∘
∘ ∘
∘
ℝℝ
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를 으로 나누면 나머지가 이다
ℕ
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ℕ
ℕ
ℕ
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ℤℤ
ℤ
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| The Axioms of Set Theory
ꊱ
ꊲ
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․
ℝ
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∘
―
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ℝ ℝ
ℝ ℝ ℝ
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ℝ ℙ ℝ ℝ
ℙ ℙ
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ℕ ℕ ℕ ℕ
ℕ ℚ ℚ ℕ
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| Image and Composition of Functions
∘ ∘
∘
∘
∘ ∘
∘
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∘ ∘ ∘ ∘
∘ ∘ ∘ ∘ ∘
∘ ∘ ∘
∘ ∘
∘ ∘ ∘ ∘
∘ ∘
∘ ∘ ∘ ∘
ℝ ∘ ∘
∘
∘
∘ ∘
∘
∘
∘
∘
∘ ∘
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∘ ∘
∘ ∘
∘
∘
∘
∘
∘
∘
∘
∘
∘
∘
∘ ∘
∘
∘ ∘
∘
∘ ∘
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∘
∘
∘ ∘
∘ ∘
∘ ∘
∘ ∘
∘
∘
∘
∘
∘ ∘
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| The Natural Numbers
ℕ
ℕ
ℕ ℕ
ℕ
ℕ ℕ
ℕ ℕ
ℕ ℕ
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ℕ ℕ
ℕ
ℕ
ℕ
ℕ
ℕ ℕ ℕ
ℕ ℕ
ℕ
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ℕ
ℕ
ℕ ℕ
ℕ
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ℕ
ℕ
ℕ ℕ
ℕ
ℕ
ℕ
ℕ
ℕ
ℕ
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―
ℕ
ℕ
ℕ
ℕ
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ℕ ⋅
⋅ ⋅ ⋅
⋅ ℕ
⋅
⋅ ⋅ ⋅
ℕ
ℕ
⋅
⋅
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ℕ
ℕ
ℕ
ℕ
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ℕ
ℕ
ℕ ℕ
ℕ
ℕ ℕ ℕ
ℕ
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ℕ ℕ ℕ
ℤ ℤ ℤ ℚ
ℝ ℚℕ
ℝ ℂ ℝ ℝ ℂ
ℕ ℕ
ℕ
ℕℕ
ℕ ℕ
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| The Ordered Sets
ℝ
ℝ
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ℕ ℕ
ℝ ℚ
ℂ ℝ
ℂ ℝ
ℝ ℂ
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↦
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∘
≊
≊ ≊ ≊ ≊ ≊ ≊
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ℕ
ℝ
ℝ ℝ
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ℕ
ℚ ℚ
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≊ ≊
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| Deeper Properties of Ordered Sets
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ℕ
ℚ ℚ
ℚ
ℚ
ℚ
ℝ
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ℕ
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∘
∘
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≊
≊ ≊
≊
≊
≊ ≊
≊ ≊
≊
≊
≊ ≊
≊
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| The Axiom of Choice
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― ―
― ― ― ―
―
―
―
―
―
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―
― ―
―
―
―
―
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ℤ ℤ
ℤ
ℕ ℕ ⊳
⊳ ⊳
⊳
⊳
⊳
⊳
⊳
⊳ ⊳
⊳
⊳
⊳
ℚ ⊳
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∘
∘
∘
∘
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∘
∘
⊰
⊰
⊰
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ℕ
ℕ
ℕ
ℕ ℕ
ℕ
ℝ
ℝ ℝ
ℝ ℂ ℝ
8/17/2019 Alice Mathscript Set Theory 2007
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ℂ ℝ ℝ
ℝ ℝ ℝ ℂ ℝ ℝ
ℕℤℚℚℝℂ
ℝ
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∘
ö
≼
≼
∘
ℕ
ℕ
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∘
∘
≼
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∘∘
∘∘ ∘∘
ℕ ℕ
ℕ ℕ
ℕ ℕ
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| Deeper Properties of Infinite Sets
ℕ
ℕ
ℕ
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ℕ
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ℕ
∘ ℕ ℕ
≊ ℕ ≊
ℕ ℕ ℕ
ℕℕ ℕ ⋅
ℕ
ℕ ℕ
ℕℕ ℕ ℕ
ℕ ℕ ℕ ℕ ℕ
ℕ
ℕ ℕ ℕ
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ℕ
ℕ
ℕ ℕ ℕ
ℕℕ
ℕ ℕ
ℕ
ℕℕ
ℕ ℕℕ ∘ ℕ
ℕ
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ℚ
ℕ ℕ
ℚ ℕℕ
ℕ ℕ ℚ
ℚ
ℚℚℚ
ℕ ℚ
ℝ
ℕ
ℕ
ℕ
8/17/2019 Alice Mathscript Set Theory 2007
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∘ ∘
∘ ∘ ∘
∘
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ℕ ℕ
ℕ
ℕ
ℕ
ℕ
ℝ ℝ
ℝ
8/17/2019 Alice Mathscript Set Theory 2007
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| The Cardinal Numbers
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ˆ ˆ
ˆ
ˆ ˆ
ˆ ˆ
≼
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≼
≼ ≼
≼ ≼
≼
≼
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ℕ ℵ
ℝ ϛ
ℵ ℵ ℵ ℕ ℵ ℕ
ℕ ℵ ℕ
ℵ ℵ ℕ ℕ ℕℵ
ℵϛ ϛ ϛ
ℕ ℵ ϛ ℕ ℕ ℝ
ϛℵ ϛ ℕ ℝ ϛ
ℵ ϛ ϛ
ℵ ℕ ϛ ℝ ℵ ϛ
ℝ ℚ
ℝ ℚ
ϛ ℚ ℵ ϛ
ℵ
ℕ ℝ
ℕ
ℕ
ℕ
ℕ ℝ
ℵ ϛ
ℵϛ
ℕ ℕℕℝ ℵ ϛ ℵ
ϛ
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ℵ
ℵ
ℵ ℵ
ℵ
≼
≼
ℵ ℵ
ℵ
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| Deeper Properties of Cardinal Numbers
ℵ ϛ ϛ
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ϛϛϛ
ℵ ℵ ℵ ℵϛ
ϛϛ ℵ
ℵ ℵ ℵ
ℵ ϛ
ϛϛ ϛ
ϛϛ ϛ ℵ ϛ
ℵ ℵ ℵ ϛϛ ϛ
ϛϛϛ ℵ
ℵ ℵℵ
ℵ
ℵϛ
ℝ ℝ
ℝ ℝ ℝℝ ℝ
ℝ ϛϛ
ℵ ϛ
ℵϛ
ϛ ϛ
ℝ
ℝ ℝ ℚ ℝ ϛ
ℝ ℝ ℚ ℚ ℚ
ℚ
ℝ ℝ ℝ ℚ
ℝ ℝ ℝ ℝ
ℚ ℝ
ℝ ℝ ℚ ℝ ℝℚϛℵ ℵ
ℵ
ℵℵ
ℵϛ
ℝ ℝ ℝ ℝ
ϛ ℝ ℝ ℝ ℝ
ℝ
ϛ ℝ ℝ
ℝ ℝ ℝ ℝ
ϛ ℝ ℝ ℝ ℝ ℚ ℝϛ
ℝ ℝ ℚ ℝ ϛ
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ℝ ℝ ℝ ϛ
ℝ ℝ ℝ ℝ ℝ ℝ
ϛ ℝ ℝ ℝ ℝ ℝ ℝ
ℝ ℝ ϛ
ℍ
ϛ ℍϛℵ
ℵ ℵ
ϛ
ℍ ϛ ϛ
ℝ ϛ
ℝ ℝ ϛ ϛ
ϛ ϛ
ℵ ϛ ϛ ϛ ϛ
ϛϛ
ℵϛ
ℵ ϛ
ϛ ℝ
ℝ ℝ
ℝ ℝ ℝ
ℵ ϛ
ℵ
ϛ
ϛ
ℵ
ϛ
ϛϛ
ϛ ϛ
ϛ
ℵ
ℵ
ℵ
8/17/2019 Alice Mathscript Set Theory 2007
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⃠
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ℕ
8/17/2019 Alice Mathscript Set Theory 2007
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ℵ
ℵ ϛ
ℝ ℝ
ℵ ϛ ℵ ϛ
ö
8/17/2019 Alice Mathscript Set Theory 2007
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8/17/2019 Alice Mathscript Set Theory 2007
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ℤ ℤ
ℤ ℕ ℕ
ℤ ℤ
ℤ
ℤ
ℤ
ℤℤ ℤ
ℤ ℤ ℤ
ℤ
ℚ ℚ
ℚ ℤ ℤ
ℚ ℚ
ℚ
ℚ ℚ
ℚℚ ℚ
ℚ ℚ ℚ
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ℚ
ℕℤℚ
8/17/2019 Alice Mathscript Set Theory 2007
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ℕ
ℚ
ℕ
ℝ
ℝ ℚ
ℕ
ℝ ℝ
ℝ
ℚ ℕ
ℝ ℝ
ℝ
ℝℝ ℝ
8/17/2019 Alice Mathscript Set Theory 2007
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ℝ
ℚ ℕ
ℝ
ℝ ℝ
ℝ
ℝ
ℝ ℝ
ℝ ℝ
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ℝ ⋅ ℝ
ℝ ⋅ ⋅
ℝ ⋅ ⋅ ⋅ ⋅
ℝ ℝ ⋅
ℝ ℝ ⋅
ℝ ⋅ ⋅ ⋅
ℙ
ℙ ℙ ⋅ ℙ
ℝ ℙ ℙ
ℝ ℙ ℙ
ℝ
ℝ
ℝ ℝ
ℂ ℝ ℝ
ℕℤℚℝℂ
8/17/2019 Alice Mathscript Set Theory 2007
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8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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ℕ
ℕ
ℕ
ℕ
ℚ
ℕ
ℚ ℝ
ℕ ℚ
ℝ
8/17/2019 Alice Mathscript Set Theory 2007
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ℕ
ℕ
8/17/2019 Alice Mathscript Set Theory 2007
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―
―
―
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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―
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
ö
8/17/2019 Alice Mathscript Set Theory 2007
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8/17/2019 Alice Mathscript Set Theory 2007
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8/17/2019 Alice Mathscript Set Theory 2007
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