17 - Bijections and Introduction Cardinality Discrete...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Introduction Bijections and Cardinality Discrete Mathematics Andrei Bulatov
Background image of page 1

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

View Full DocumentRight Arrow Icon
Discrete Mathematics - Cardinality 17-2 Previous Lecture Functions Describing functions Injective functions Surjective functions Bijective functions
Background image of page 2
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.
Background image of page 3

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

View Full DocumentRight Arrow Icon
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
Background image of page 4
Discrete Mathematics - Cardinality 17-5 89 100 90 80 70 49 0 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. Adams
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/14/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

Page1 / 16

17 - Bijections and Introduction Cardinality Discrete...

This preview shows document pages 1 - 6. Sign up to view the full document.

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