35 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] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [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] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
6685 | 'Subjectivism' is an extension of relativism from the social group to the individual [Graham] |
6699 | The chain of consequences may not be the same as the chain of responsibility [Graham] |
6698 | Negative consequences are very hard (and possibly impossible) to assess [Graham] |
6700 | We can't criticise people because of unforeseeable consequences [Graham] |
6704 | Egoism submits to desires, but cannot help form them [Graham] |
6701 | Rescue operations need spontaneous benevolence, not careful thought [Graham] |
6693 | 'What if everybody did that?' rather misses the point as an objection to cheating [Graham] |
6691 | It is more plausible to say people can choose between values, than that they can create them [Graham] |
6688 | Life is only absurd if you expected an explanation and none turns up [Graham] |
6705 | Existentialism may transcend our nature, unlike eudaimonism [Graham] |
6690 | A standard problem for existentialism is the 'sincere Nazi' [Graham] |
6689 | The key to existentialism: the way you make choices is more important than what you choose [Graham] |
6706 | The great religions are much more concerned with the religious life than with ethics [Graham] |
6709 | Western religion saves us from death; Eastern religion saves us from immortality [Graham] |