Strict order relationship

They are denoted by the symbol

· Transitivity; If x < Y and Y < Z , then X < Z ;

· Anti-reflexivity; If X < Y , then X ¹ Y , that is, it is performed only for non-coinciding objects;

· Asymmetry; of two relationships X < Y and Y < X One is always wrong.

A strict order relationship is characteristic of various kinds of hierarchies with the subordination of one object to another. A typical example of a strict order relationship is the relationship “be older”, etc., corresponding to mathematically strict inequality or strict inclusion.

If a set of a perfectly strict order is given on the set M , then its elements can be numbered by ordinal numbers 1, 2, ..., N , ..., i.e. each number I can be associated with some element X I Î m . An ordered set in this way is called a Sequence (finite or infinite). The element X I Î M is called the Member of the sequence with the index (number) I. In this case, the ratio X I < X J will be satisfied only if I < J . If the order on the set is not perfect, that is, the set is partially strictly ordered, then its elements cannot be numbered so that the higher numbers correspond to the higher elements. Therefore, if the elements of a set are numbered, then the set is perfectly strictly ordered. The numbering of the elements of the set establishes a very strict order on it.