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'works', 'Knowledge and the Philosophy of Number' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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Real numbers are ratios of quantities, such as lengths or masses [Frege]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
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Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
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