MATH 113 Lecture 2: Equivalence Relations and Modulo Congruence
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Example s is a set consider e lx x s. This is called the equalityrelation and itself is called arelation ship. Notation set on a if relation i x x for all x c s y then y x ii iii if if x y and y z then x an equivalence reflexive symmetric. Congruence modulo n h c k related to b if claims this is an equivalence is a i a c 7l a b if ii ii of a b and a a o and. 3 all odd numbers all even numbers are congruent n are congruent. 7l exek x is odd u exeze x is even. Definition a earldom of subsets of s in s is a called cells in exactly one cell. 2 cells in this partition of 2 set 5 10 is a such that collection of each element theorem equnate relations. Consider a portion of k with a of division by h.
