14126 | Order rests on 'between' and 'separation' [Russell] |
14127 | Order depends on transitive asymmetrical relations [Russell] |
11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |