In mathematics,
inequalities
compare numbers and
expressions that are
not equal to
one another.
Generally, the
following symbols
are used for
comparison:
, 
, 
, 
.
Each of these
symbols compares the
relative size of two
numbers
to show which number
is bigger, and which
number is
smaller.
Inequalities
are important
because they are
common to
everyday life
experiences.
People
intuitively use the
concept of
inequality to
compare options and
make choices based
on relative
value.
For example, a
person may ask
themselves:
"Can I buy a
new car with $10,000
if a new car costs
$11,000?" The
comparison of these
choices is an
inequality. One
number is smaller
than the other
number.
Automatic control
systems rely on this
concept as well. A
thermostat uses an
inequality
(comparing
temperatures) to
decide whether to
turn on a heater or
air conditioner. For
example, the
thermostat may turn
on an air
conditioner when the
temperature rises
above 85 degrees (or
turn off the air
conditioner when the
temperature falls
below 80
degrees).
The
Properties of
Inequality
of Real Numbers -
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Transitive
Property of
Inequality
-
The
Transitive
Property of
Inequality is
similar to the
Transitive
Property of
Equality
described under
"Equivalence"
Relationships.
However, there
are a
large
number of
possible
variations
when applying
the Transitive
Property to
inequalities.
This being
said, the logic
can be
illustrated as
follows: if a
number is less
than or equal
to a second
number, and the
second number
is less than or
equal to a
third number,
then the first
number is also
less than or
equal to the
third
number.
Examples
follow.
However, the
examples shown
below are not
inclusive.
There are many
more
possibilities
which could be
shown.
a =
any real
number,
b =
any real
number,
c =
any real
number
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If a
b
and
b
c,
then
a
c
If 5
1
and
1
0,
then
5
0
If
15
17
and
17
19,
then
15
19
