38 ideas
| 23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
| 23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
| 23075 | A text explained ceases to be a text [Cioran] |
| 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] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 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] |
| 23077 | The word 'being' is very tempting, but in fact means nothing at all [Cioran] |
| 23068 | People who really believe anti-realism don't bother to prove it [Cioran] |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| 23076 | If people always acted without words we would take them for robots [Cioran] |
| 23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
| 23071 | We could only be responsible if we had consented before birth to who we are [Cioran] |
| 23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
| 23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| 23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
| 23067 | Suicide is pointless, because it always comes too late [Cioran] |
| 5467 | Euler said nature is instrinsically passive, and minds cause change [Euler, by Ellis] |
| 23063 | The first man obviously found paradise unendurable [Cioran] |