And order was established

The German mathematician Georg Cantor (1845–1918) paved the way for the general theory of order relations while studying certain classes of totally ordered sets as part of his research into trigonometric series. His compatriot Felix Hausdorff (1868–1942) then developed the theory further in the 1910s. Later, with advances in axiomatic set theory, lattice theory and then the study of discrete structures, the notion of order assumed its rightful place in pure and applied mathematics.

Order relations ---------------------

Behind this seemingly simple notion lie three defining properties. In a set P, a binary relation (that is, a relation between two elements of P), denoted by $\mathrm{\Re }\backslash Re$, is called an order relation if:

• it is reflexive: for every x in P, x $\mathrm{\Re }\backslash Re$ x;

• it is antisymmetric: if x and y belong to P and x $\mathrm{\Re }\backslash Re$ y and y $\mathrm{\Re }\backslash Re$ x, then x = y;