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
• a b
• or a b
• or a b