قواعد اولیه (Basic properties) مربوط به نامساوی ها (Inequalities)

در اینجا، تعدادی از قواعد مربوط به نامساوی ها (Inequalities) را ذکر می کنیم :

\[ a < b \quad \Rightarrow \quad b > a \]

\[ \left. {\begin{array}{*{20}{c}} {a \le b}\\ {b \le a} \end{array}} \right\} \quad \Rightarrow \quad a = b \]

\[ \left. {\begin{array}{*{20}{c}} {a \le b}\\ {b \le c} \end{array}} \right\} \quad \Rightarrow \quad a \le c \]

\[ \left. {\begin{array}{*{20}{c}} {a < b}\\ {b \le c} \end{array}} \right\} \quad \Rightarrow \quad a < c \]

\[ \left. {\begin{array}{*{20}{c}} {a \le b}\\ {b < c} \end{array}} \right\} \quad \Rightarrow \quad a < c \]

\[ \left. {\begin{array}{*{20}{c}} {a < b}\\ {c < d} \end{array}} \right\} \quad \Rightarrow \quad a + c < b + d \]

\[ \left. {\begin{array}{*{20}{c}} {a < b}\\ {c = d} \end{array}} \right\} \quad \Rightarrow \quad a + c < b + d \]

\[ \left. {\begin{array}{*{20}{c}} {a \le b}\\ {c > 0} \end{array}} \right\} \quad \Rightarrow \quad ac \le bc \]

\[ \left. {\begin{array}{*{20}{c}} {a \le b}\\ {c < 0} \end{array}} \right\} \quad \Rightarrow \quad ac \ge bc \]

\[ 0 < a \le b \quad \Rightarrow \quad \frac{1}{a} \ge \frac{1}{b} \]

\[ a \le b < 0 \quad \Rightarrow \quad \frac{1}{a} \ge \frac{1}{b} \]