This preview shows pages 1–2. Sign up to view the full content.
Chapter 2 – Countable and Uncountable Sets
Equivalence and Cardinality
Pg 18
We say that two sets A and B are
equivalent (A~B)
if there is a onetoone correspondence
between them.
Equivalence you need:
(1)onetoone and
(2)onto.
A function f from A to B is called
onetoone (injective)
if whenever f(a) = f(b), then a = b. No
element of B is the image of more than one element of A
A function f from A to B is called
onto (surjective)
if for all b in B there is an a in A such that
f(a) = b. All elements in B are used.
Bijective
is when both onetoone and onto.
Equivalent sets have the same
cardinality
(number of elements).
A is called
finite
if A = { } or if A is equivalent to the set {1, 2, … n} for some n
ϵ
N, otherwise
A is
infinite
.
An infinite set A is said to be
countable
(or
countably infinite
) if A is equivalent to N.
Pg 19
Countable Sets
– either countably infinite or finite.
Well Ordered
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Higdon
 Sets

Click to edit the document details