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

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

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

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

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

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

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

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

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

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

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

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

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