Combining Texts
Ideas for
'works', 'Continuity and Irrational Numbers' and 'Philosophy of Mathematics'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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17611
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We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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10572
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A cut between rational numbers creates and defines an irrational number [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
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17612
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Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
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18087
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If x changes by less and less, it must approach a limit [Dedekind]
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6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
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10885
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Computer proofs don't provide explanations [Horsten]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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10881
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The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
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