Combining Texts
Ideas for
'Thinking About Mathematics', 'The Doctrine of Necessity Examined' and 'Intro to Gdel's Theorems'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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10599
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For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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8763
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The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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10610
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The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
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18249
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Cauchy gave a formal definition of a converging sequence. [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
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10619
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The truths of arithmetic are just true equations and their universally quantified versions [Smith,P]
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