13 ideas
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [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] |
| 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] |
| 15584 | I say the manifestation of Being needs humans, and humans only exist as reflected in Being [Heidegger] |
| 5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
| 13159 | Only God sees contingent truths a priori [Leibniz] |
| 5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
| 5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |