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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Trichotomy
Property of
Inequality

The property of
Trichotomy
states that
when any
two numbers are
compared, there
are only three
possible
outcomes
:
•
The
first
number
is
smaller
than the
second
number
•
Both
numbers
are
equal
•
The
second
number
is
smaller
than the
first
number
This can be
expressed
algebraically
as follows:
a =
any real
number,
b =
any real
number