more from this thinker | more from this text
Full Idea
The two sources of order are 'between' and 'separation'.
Gist of Idea
Order rests on 'between' and 'separation'
Source
Bertrand Russell (The Principles of Mathematics [1903], §204)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.216
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] |
13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
13458 | A partial ordering becomes 'total' if any two members of its field are comparable [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] |