Open the course syllabus in your preferred browser 2. Since f is a partition, for each x in s there is one and only one set of f which contains x. A partition of a set x is a set p fc i x ji 2ig such that i2i c i x covering property 8i 6 s c. A relation r on a set x is said to be an equivalence relation if. Define a relation on s by x r y iff there is a set in f which contains both x and y. Les equivalences entre diplomes sanitaires et sociauxsociaux. This is an equivalence relation for rather trivial reasons.
Relation exercice 1 soit rla relation binaire dans e f0. There is a theorem, proved in an advanced course in set theory, that says that any set. Select your third party installed pdf printer bullzip or cutepdf 4. Pour illustrer ce cours nous considererons trois exemples. Then r is an equivalence relation and the equivalence classes of r are the sets of f. Equivalence relations and functions october 15, 20 week 14 1 equivalence relation a relation on a set x is a subset of the cartesian product x. Let r be the relation on the set r real numbers defined by xry iff x. Consequently,scan be partitioned into disjoint equivalence classes in s for example, zis the disjoint union of the equivalence classes 0 3, 1 3, and 2 3.
Indication 2 il faut trouver lerreur dans ce raisonnement, car bien sur. We define a rational number to be an equivalence classes of elements of s, under the equivalence relation. The equality equivalence relation is the finest equivalence relation on any set, while the universal relation, which relates all pairs of elements, is the coarsest. Ces notions ne sont pas fondamentalement difficiles et ce cours propose une. On appelle relation dequivalence toute relation binaire reflexive, transitive et symetrique.