MAT425 Real Analysis L4 Prof. Thistleton Orderings Cross Products, . We can define a relation from a set A to a set B as a subset of . We define a relation in A simply as a subset of . R is symmetric if, . R is antisymmetric if, .
R is transitive if, .
A is a relation which is reflexive, antisymmetric, and transitive. An ordering on A is linear if any two elements of A are comparable. Show that the relation defined on the reals and denoted is a linear ordering. The following definition is from our text. Linear Ordering Let S be a set.