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] |
5495 | Instances of pain are physical tokens, but the nature of pain is more abstract [Putnam, by Lycan] |
8063 | Baumgarten founded aesthetics in 1750 [Baumgarten, by Tolstoy] |
8118 | Beauty is an order between parts, and in relation to the whole [Baumgarten, by Tolstoy] |
8117 | Perfection comes through the senses (Beauty), through reason (Truth), and through moral will (Good) [Baumgarten, by Tolstoy] |