35 ideas
6259 | Why can't a wise man doubt everything? [Montaigne] |
6263 | No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne] |
23122 | Montaigne was the founding father of liberalism [Montaigne, by Gopnik] |
6258 | Virtue is the distinctive mark of truth, and its greatest product [Montaigne] |
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] |
6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
6260 | Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne] |
6261 | The soul is in the brain, as shown by head injuries [Montaigne] |
7496 | Rules and duties are based on the will, as that is all we control [Montaigne] |
7495 | Apart from the fear, dying is an easy duty [Montaigne] |
22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
20482 | Virtue inspires Stoics, but I want a good temperament [Montaigne] |
20480 | There is not much point in only becoming good near the end of your life [Montaigne] |
20481 | Nothing we say can be worse than unsaying it in the face of authority [Montaigne] |
20479 | People at home care far more than soldiers risking death about the outcome of wars [Montaigne] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |