14 ideas
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |