Introduction to Set Theory
James H. Steiger
,Sets
Definition. A Set is any well defined collection of
“objects.”
Definition. The elements of a set are the objects in a
set.
Notation. Usually we denote sets with upper-case
letters, elements with lower-case letters. The following
notation is used to show set membership
x means
A that x is a member of the set A
x means
A that x is not a member of the set A.
, Ways of Describing Sets
List the elements
A= 1,2,3,4,5,6
Give a verbal description
“A is the set of all integers from 1 to 6,
inclusive”
Give a mathematical inclusion rule
A= Integers x 1 x 6
James H. Steiger
,Sets
Definition. A Set is any well defined collection of
“objects.”
Definition. The elements of a set are the objects in a
set.
Notation. Usually we denote sets with upper-case
letters, elements with lower-case letters. The following
notation is used to show set membership
x means
A that x is a member of the set A
x means
A that x is not a member of the set A.
, Ways of Describing Sets
List the elements
A= 1,2,3,4,5,6
Give a verbal description
“A is the set of all integers from 1 to 6,
inclusive”
Give a mathematical inclusion rule
A= Integers x 1 x 6
