Quote: an ordering relation has three properties: x not y<x; x<y and y x<z; and, either x<y or y<x

Quotation

we require that the ordering relation should have three properties :-- (1) if x precedes y, y must not also precede x. ... A relation having this first property is called asymmetrical. (2) If x precedes y and y precedes z, x must precede z. ... [p. 32] A relation having our second property is called transitive. (3) Given any two terms of the class which is to be ordered, there must be one which precedes and the other which follows. ... A relation having this third property is called connected.   Google-1   Google-2

Published before 1923

Related Topics

Group: mathematics   (23 topics, 554 quotes)
Topic: ordered data types (8 items)