Editing Order theory (section)

==History==
As explained before, orders are ubiquitous in mathematics. However, the earliest explicit mentionings of partial orders are probably to be found not before the 19th century. In this context the works of [[George Boole]] are of great importance. Moreover, works of [[Charles Sanders Peirce]], [[Richard Dedekind]], and [[Ernst Schröder (mathematician)|Ernst Schröder]] also consider concepts of order theory.

Contributors to [[ordered geometry]] were listed in a 1961 [[textbook]]:
{{blockquote|text=It was [[Moritz Pasch|Pasch]] in 1882, who first pointed out that a geometry of order could be developed without reference to measurement. His system of axioms was gradually improved by [[Giuseppi Peano|Peano]] (1889), [[David Hilbert|Hilbert]] (1899),  and [[Oswald Veblen|Veblen]] (1904).|author=[[H. S. M. Coxeter]]|title=Introduction to  Geometry}}

In 1901 [[Bertrand Russell]] wrote "On the Notion of Order"<ref>[[Bertrand Russell]] (1901) [[Mind (journal)|''Mind'']] 10(2)</ref> exploring the foundations of the idea through generation of [[serial relation|series]]. He returned to the topic in part IV of ''[[The Principles of Mathematics]]'' (1903). Russell noted that [[binary relation]] ''aRb'' has a sense proceeding from ''a'' to ''b'' with the [[converse relation]] having an opposite sense, and sense "is the source of order and series." (p 95) He acknowledges [[Immanuel Kant]]<ref>[[Immanuel Kant]] (1763) ''Versuch den Begriff der negativen Grosse in die Weltweisheit einzufuhren''</ref> was "aware of the difference between logical opposition and the opposition of positive and negative". He wrote that Kant deserves credit as he "first called attention to the logical importance of asymmetric relations."

The term ''poset'' as an abbreviation for partially ordered set is attributed to [[Garrett Birkhoff]] in the second edition of his influential book ''Lattice Theory''.{{sfn|Birkhoff|1940|p=1}}<ref>{{Cite web|url=http://jeff560.tripod.com/p.html|title=Earliest Known Uses of Some of the Words of Mathematics (P)|website=jeff560.tripod.com}}</ref>