Strict Weak Ordering

A strict weak ordering has the following properties. For all ''x'' and ''y'' in ''S'',

Irreflexive : ''x'' R ''x'' is false

Antisymmetric : if ''x'' ≠ ''y'' and ''x'' R ''y'' then not ''y'' R ''x''

Transitive : if ''x'' R ''y'' and ''y'' R ''z'' then ''x'' R ''z''

transitivity of equivalence: If ''x'' is equivalent to ''y'' (under the equivalence relation defined above) and ''y'' is equivalent to ''z'', then ''x'' is equivalent to ''z''.

Note that this list of properties is somewhat redundant, as antisymmetry follows readily from irreflexivity and transitivity.

A strict weak ordering is a Strict Partial Order that satisfies transitivity of equivalence.

Example: a
Example of a strict partial order that is not a strict weak order: a
An example of a strict weak ordering is the Less Than relationship over Real Numbers .

	CATEGORIES ABOUT STRICT WEAK ORDERING

	order theory

	integer sequences

	mathematical relations

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Strict Weak Ordering

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