28 ideas
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
3654 | The pineal gland links soul to body, and unites the two symmetrical sides of the body [Descartes, by PG] |
4015 | For Descartes passions are God-given preservers of the mind-body union [Descartes, by Taylor,C] |
4313 | Are there a few primary passions (say, joy, sadness and desire)? [Descartes, by Cottingham] |
23989 | There are six primitive passions: wonder, love, hatred, desire, joy and sadness [Descartes, by Goldie] |
20037 | Merely willing to walk leads to our walking [Descartes] |
16763 | We don't die because the soul departs; the soul departs because the organs cease functioning [Descartes] |
4016 | Descartes makes strength of will the central virtue [Descartes, by Taylor,C] |
19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |