This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Definitions and Theorems Chapter 0 1. Cartesian Product 2. Relation, domain, image 3. Function 4. Composition of two functions 5. injective (11), surjective (onto), bijective, inverse function 6. Principle of Mathematical Induction (p 12) 7. Equivalence relation: A relation R on a set A is said to be an equivalence relation if: (a) (reflexivity) For each x A we have ( x,x ) R (b) (symmetry) If ( x,y ) R then ( y,x ) R (c) (transitivity) If ( x,y ) R and ( y,z ) R , then ( x,z ) R If ( x,y ) R then we write x y 8. Let U be a family of sets that includes at least R and all of its subsets. On this set we define an equivalence relation as follows: A B if there exists a bijection f : A B . If A B then we say A and B are (cardinally) equivalent . 9. Let S be a set. Its power set P is the family of all subsets of S . Sometimes the power set of S is denoted by 2 S . Hence P 2 S := { A  A S } ....
View Full
Document
 Spring '07
 thieme
 Mathematical Induction

Click to edit the document details