Combining Texts

All the ideas for 'fragments/reports', 'Elements of Set Theory' and 'Theories of Everything'

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27 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / b. Heat
20624 Work degrades into heat, but not vice versa [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
20623 First Law: energy can change form, but is conserved overall [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
20625 Third Law: total order and minimum entropy only occurs at absolute zero [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
20622 All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close]
20628 The electric and magnetic are tightly linked, and viewed according to your own motion [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
20635 The general relativity equations relate curvature in space-time to density of energy-momentum [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
20642 Photon exchange drives the electro-magnetic force [Close]
20627 Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close]
20630 Light isn't just emitted in quanta called photons - light is photons [Close]
20637 In general relativity the energy and momentum of photons subjects them to gravity [Close]
20629 Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close]
20632 In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
20639 Quantum fields contain continual rapid creation and disappearance [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
20641 Electrons get their mass by interaction with the Higgs field [Close]
20631 Dirac showed how electrons conform to special relativity [Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
20626 Modern theories of matter are grounded in heat, work and energy [Close]
27. Natural Reality / B. Modern Physics / 5. Unified Models / a. Electro-weak unity
20633 The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close]
27. Natural Reality / C. Space / 6. Space-Time
20640 Space-time is indeterminate foam over short distances [Close]