Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'What Required for Foundation for Maths?' and 'Physics'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9790
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Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
22962
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Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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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 / 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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18090
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Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
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17797
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Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
22929
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Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
22930
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Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
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18833
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A continuous line cannot be composed of indivisible points [Aristotle]
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