Combining Texts
Ideas for
'Individuals without Sortals', 'Intro to Gdel's Theorems' and 'Cours d'Analyse'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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 / g. Real numbers
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 / 4. Using Numbers / d. Counting via concepts
17518
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Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
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17516
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If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
10619
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The truths of arithmetic are just true equations and their universally quantified versions [Smith,P]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18085
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Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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