1. Chapter 2: SETS

2. A set is a collection of objects.
2.1 Set Concepts p. 45
Def:
A set is a collection of objects.
Elements or members are objects in the set.
Symbol: means “is an element of”
means “is not an element of”
3. A set is well-defined if its contents can be clearly determined.
Example: The set of U.S. presidents.
Non-example: The set of the three best movies.

3. Note: Methods used to indicate a set.
Description- describes a set in words
Roster form - lists the elements of a set inside braces {}
Set-builder notation - uses words and symbols to show the condition(s) an element must meet to be a member of the set
Examples 1-6

4. Note:
1. A set is finite if it contains no elements or the number of elements is a natural number.
(the set of students taking this class)
2. A set that is not finite is infinite. (the set of counting numbers)

5. Def: Set A is equal to set B, symbolized A = B, if and only if set A and set B contain exactly the same elements.
Ex: If set A = {1, 2, 3} and set B = {3, 1, 2}, then A = B.
Def: The cardinal number of set A, symbolized n(A), is the number of elements in set A.
Ex: Set A = {1, 2, 3} and set B = {England, Brazil, Japan}
Def: Set A is equivalent to set B if and only if n(A) = n(B).
Ex: D = {a, b, c} and E = {apple, orange, pear}
Question: Are sets D and E equal?

6. Note: Two sets that are equivalent can be placed in
one-to-one correspondence. (every element of one set can be matched with exactly one element of another set)
Def: The set that contains no elements is the called the empty set or null set.
Symbol: { } or
Def: A universal set is a set that contains all the elements for any specific discussion.
Symbol: U
Example: U = {1, 2, 3, 4,…., 10}