48 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 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] |
| 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] |
| 20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
| 20641 | Electrons get their mass by interaction with the Higgs field [Close] |
| 20631 | Dirac showed how electrons conform to special relativity [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] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |