Combining Texts
Ideas for
'Defending the Axioms', 'The Iliad' and 'On the Infinite'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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12461
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We believe all mathematical problems are solvable [Hilbert]
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12456
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I aim to establish certainty for mathematical methods [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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9633
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No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
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12460
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We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
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12462
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Only the finite can bring certainty to the infinite [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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12455
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The idea of an infinite totality is an illusion [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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17615
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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12457
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There is no continuum in reality to realise the infinitely small [Hilbert]
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