Combining Texts
Ideas for
'Frege's Concept of Numbers as Objects', 'Hat-Tricks and Heaps' and 'What Required for Foundation for Maths?'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13861
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Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13892
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One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
17784
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Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
17782
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Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
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17781
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Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
13867
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Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17799
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Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
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17797
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Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
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