12 ideas
| 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] |
| 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] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
| 9409 | Laws are the best axiomatization of the total history of world events or facts [Lewis, by Mumford] |
| 9423 | If simplicity and strength are criteria for laws of nature, that introduces a subjective element [Mumford on Lewis] |
| 9424 | A number of systematizations might tie as the best and most coherent system [Mumford on Lewis] |