Combining Texts

All the ideas for 'Through the Looking Glass', 'Universals' and 'The Art of the Infinite'

expand these ideas     |    start again     |     specify just one area for these texts

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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 / A. Nature of Existence / 3. Being / e. Being and nothing

21982

I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]

8. Modes of Existence / D. Universals / 1. Universals

8495	The distinction between particulars and universals is a mistake made because of language [Ramsey]

8493	We could make universals collections of particulars, or particulars collections of their qualities [Ramsey]

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism

8494	Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey]

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

15713

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