17h - Introduction Bijections and Cardinality Discrete...

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: Introduction Bijections and Cardinality Discrete Mathematics Andrei Bulatov Discrete Mathematics - Cardinality 17-2 Previous Lecture Functions Describing functions Injective functions Surjective functions Bijective functions Discrete Mathematics - Cardinality 17-3 Properties of Functions A function f is said to be one-to-one , or injective , if and only if f(a) = f(b) implies a = b. A function f from A to B is called onto , or surjective , if and only if for every element b ∈ B there is an element a ∈ A with f(a) = b. A function is called a surjection if it is onto. A function f is a one-to-one correspondence , or a bijection , if it is both one-to-one and onto. Discrete Mathematics - Cardinality 17-4 Composition of Functions Let g be a function from A to B and let f be a function from B to C. The composition of the functions f and g, denoted by f ○ g, is the function from A to C defined by ( f ○ g)(a) = f( g( a )) g f a g(a) f(g(a)) g(a) f(g(a)) (f ○ g)(a) f ○ g A B C Discrete Mathematics - Cardinality 17-5 89 100 90 80 70 49 … 79 69 50 Composition of Functions (cntd) Suppose that the students first get numerical grades from 0 to 100 that are later converted into letter grade....
View Full Document

This note was uploaded on 05/18/2010 for the course MACM MACM 101 taught by Professor Andreibulatov during the Spring '10 term at Simon Fraser.

Page1 / 3

17h - Introduction Bijections and Cardinality Discrete...

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