1
SET DEFINITIONS
Item
Definition
Designation
example
set
collection of objects
{1,3, 5,7}
my deck of cards is a
set of cards
Empty set
a set has nothing in it
\
Subset
A is a subset of B, designated by
A
B or B
A if all members of
A are members of B
U = {x
Z
: P(x)} where
P(x)
means 1 ≤ x ≤ 7, x is odd this
uses subsets to define the sets
Equal sets
Two sets are equal if they
contain the same elements, i.e.,
A
B and B
A
Proper subset
A
B and B
A
Number designations
R
or
R
collection of real numbers
<
or
Q
collection of rational numbers, that is consists of p/q where p and q are integers
Z
or
Z
collection of integers: …, -2, -1, 0, 1, 2, .
..
N
or
N
collection of positive integer (does not include 0): 1, 2, …
Intervals
Let a,b
R
(a,b) = {x
R
: a < x < b}
bounded open interval
[a,b] = {x
R
: a ≤ x ≤ b}
bounded closed interval
[a,b) = {x
R
: a ≤ x < b}
bounded half-open
interval
(a,b] = {x
R
: a < x ≤ b}
bounded half-open
interval
(a,∞) = {x
R
: x > a}
unbounded open interval
(-∞,b) = {x
R
: x < b}