Nnrelation d'equivalence cours pdf

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. Open the course syllabus in your preferred browser 2. Les equivalences entre diplomes sanitaires et sociauxsociaux. Relation exercice 1 soit rla relation binaire dans e f0. An equivalence relation on a set s, is a relation on s which is reflexive, symmetric. Pour illustrer ce cours nous considererons trois exemples. 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. 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. Describe in as simple way as possible the equivalence classes of the preceding examples which turned out to be equivalence relations. Then r is an equivalence relation and the equivalence classes of r are the sets of f. Relations dequivalence et ensemble quotient les pages perso du. Pdf based on experimental evidence, it is often said that one should give up the concept of preference. Let r be the relation on the set r real numbers defined by xry iff x.

Since f is a partition, for each x in s there is one and only one set of f which contains x. 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. Indication 2 il faut trouver lerreur dans ce raisonnement, car bien sur. On appelle relation dequivalence toute relation binaire reflexive, transitive et symetrique. A relation r on a set x is said to be an equivalence relation if.