13 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] |
10467 | Individuals consist of 'compresent' tropes [Bacon,John] |
10464 | A trope is a bit of a property or relation (not an exemplification or a quality) [Bacon,John] |
10465 | Trope theory is ontologically parsimonious, with possibly only one-category [Bacon,John] |
10466 | Maybe possible worlds are just sets of possible tropes [Bacon,John] |
23137 | Liberty without socialism is injustice; socialism without liberty is brutality [Bakunin] |