MAT371defs0

MAT371defs0 - Definitions and Theorems Chapter 0 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 (1-1), 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

Page1 / 2

MAT371defs0 - Definitions and Theorems Chapter 0 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online