14 ideas
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 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] |
| 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] |
| 8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
| 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] |
| 8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
| 8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
| 8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |