What is an "ordered set"?
Following Georg Cantor (the principal creator of set theory) we may define a set as any collection S into a whole of definite, distinct objects e (which are called the elements of S) of our perception or of our thought.
An order on S is a relation, denoted by <, with the following two properties:(i) If x is an element of S and y is an element of S, then one and only one of the statements: x < y, x = y, y < x is true.
(ii) If x, y, z are elements of S and if x < y and y < z then x < z