Combining Philosophers
Ideas for Pythagoras, Lawrence M. Krauss and Ernst Zermelo
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3 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
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For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
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Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
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