Using Inductive Reasoning to Create Inequalities

Concept

Strict vs. Non-Strict Inequality

An inequality that compares two quantities that are strictly not equal is called a strict inequality. There are two types of strict inequalities. Less Than:&< Greater Than:&> The boundary values in strict inequalities are not included in the solution set. On the other hand, an inequality that compares two quantities that are not necessarily different is called a non-strict inequality. There are two types of non-strict inequalities. Less Than or Equal To:&≤ Greater Than or Equal To:&≥ The boundary values in non-strict inequalities are included in the solution set. Consider the graphs of several examples of strict and non-strict inequalities.

Strict vs. Non-strict Inequalities shown in the number line and in the cartesian plane

It can be seen that in order to indicate strict inequalities graphically, an open point (∘) is used for number line inequalities and a dashed boundary line or curve is used for two-dimensional inequalities. To indicate non-strict inequalities graphically, a closed point (∙) is used for number line inequalities and a solid boundary line or curve is used for two-dimensional inequalities.

Exercises
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