16 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] |
| 7544 | Many people imagine that to experience is to understand [Goethe] |
| 7541 | Man never understands how anthropomorphic he is [Goethe] |
| 7543 | We gain self-knowledge through action, not thought - especially when doing our duty [Goethe] |
| 7540 | Beauty is a manifestation of secret natural laws [Goethe] |
| 18678 | Maybe final value rests on the extrinsic property of being valued by a rational agent [Korsgaard, by Orsi] |
| 7538 | The happiest people link the beginning and end of life [Goethe] |
| 7542 | The best form of government teaches us to govern ourselves [Goethe] |
| 7539 | To get duties from people without rights, you must pay them well [Goethe] |