Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, Tom Milsted and Michle Friend
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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8667
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The 'integers' are the positive and negative natural numbers, plus zero [Friend]
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8668
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The 'rational' numbers are those representable as fractions [Friend]
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8670
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A number is 'irrational' if it cannot be represented as a fraction [Friend]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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8661
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The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
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8664
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Cardinal numbers answer 'how many?', with the order being irrelevant [Friend]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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8671
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The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
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8663
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Raising omega to successive powers of omega reveal an infinity of infinities [Friend]
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8662
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The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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8669
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Between any two rational numbers there is an infinite number of rational numbers [Friend]
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