Combining Texts

All the ideas for 'fragments/reports', 'The Art of the Infinite' and 'fragments/reports'

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

15714

'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]

15715

'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being

12270

Being is one [Melissus, by Aristotle]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

3059	There is no real motion, only the appearance of it [Melissus, by Diog. Laertius]

27. Natural Reality / C. Space / 1. Void

5100	The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus]

27. Natural Reality / E. Cosmology / 2. Eternal Universe

456	Nothing could come out of nothing [Melissus]