14 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] |
5044 | Reality must be made of basic unities, which will be animated, substantial points [Leibniz] |
5045 | No machine or mere organised matter could have a unified self [Leibniz] |
5046 | The soul does know bodies, although they do not influence one another [Leibniz] |
5043 | To regard animals as mere machines may be possible, but seems improbable [Leibniz] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |