Combining Texts

All the ideas for 'fragments/reports', 'The Art of the Infinite' and 'A Universe from Nothing'

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16 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 / C. Structure of Existence / 2. Reduction
21110 An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21105 In 1676 it was discovered that water is teeming with life [Krauss]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
467 A virtue is a combination of intelligence, strength and luck [Ion]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
21109 Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
21104 General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21107 Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
21106 Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space / 2. Space
21112 Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / E. Cosmology / 3. The Beginning
21108 The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / E. Cosmology / 10. Multiverse
21111 It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]