40 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
20624 | Work degrades into heat, but not vice versa [Close] |
20623 | First Law: energy can change form, but is conserved overall [Close] |
20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
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] |
20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [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] |
20642 | Photon exchange drives the electro-magnetic force [Close] |
20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
20631 | Dirac showed how electrons conform to special relativity [Close] |
20641 | Electrons get their mass by interaction with the Higgs field [Close] |
20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
20640 | Space-time is indeterminate foam over short distances [Close] |