Combining Texts
Ideas for
'fragments/reports', 'Continuity and Irrational Numbers' and 'Grounding Concepts'
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8 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 / a. The Infinite
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17730
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Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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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 / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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17719
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Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
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17717
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Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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17724
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It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
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