Giả sử x= a/ m; y= b/ m (a, b, m thuộc Z, m> 0) và x< y

$$\begin{gathered} \mathrm{Giả} \mathrm{sử} \mathrm{x}=\frac{\mathrm{a}}{\mathrm{m}} , \mathrm{y}=\frac{\mathrm{b}}{\mathrm{m}} (\mathrm{a}, \mathrm{b}, \mathrm{m} \in \mathbf{ }\mathbf{Z}, \mathrm{m} >0) \mathrm{và} \mathrm{x}<\mathrm{y}. \mathrm{Hãy} \mathrm{chứng} \mathrm{tỏ} \mathrm{rằng} \mathrm{nếu} \mathrm{chọn} \mathrm{z}=\frac{\mathrm{a}+\mathrm{b}}{2\mathrm{m}} \mathrm{thì} \\ \mathrm{ta} \mathrm{có} \mathrm{x}<\mathrm{z}<\mathrm{y}. \end{gathered}$$