31 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] |
23279 | It is important that a person can change their character, and not just be successive 'selves' [Williams,B] |
23280 | Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B] |
23278 | For utilitarians states of affairs are what have value, not matter who produced them [Williams,B] |
19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |