Combining Texts

All the ideas for 'Purifications (frags)', 'Anthropological Studies of Classification' and 'The Art of the Infinite'

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10 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]

7. Existence / E. Categories / 1. Categories

10496

Monothetic categories have fixed defining features, and polythetic categories do not [Ellen]

10497

In symbolic classification, the categories are linked to rules [Ellen]

7. Existence / E. Categories / 5. Category Anti-Realism

10495

Continuous experience sometimes needs imposition of boundaries to create categories [Ellen]

13. Knowledge Criteria / E. Relativism / 4. Cultural relativism

10498

Classification is no longer held to be rooted in social institutions [Ellen]

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

15713

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