Ta có \(x < y \Rightarrow \dfrac{a}{m} < \dfrac{b}{m} \Leftrightarrow a < b\)
Lại có: \(x = \dfrac{a}{m} = \dfrac{{2a}}{{2m}};y = \dfrac{b}{m} = \dfrac{{2b}}{{2m}}\)
Vì \(a < b\left( {a,b \in Z} \right) \Leftrightarrow a + 1 \le b\) hay \(2a + 2 \le 2b\)
Suy ra \(2a < 2a + 1 < 2a + 2 \le 2b\) hay \(2a < 2a + 1 < 2b\)
Do đó \(\dfrac{{2a}}{{2m}} < \dfrac{{2a + 1}}{{2m}} < \dfrac{{2b}}{{2m}}\)
Suy ra \(x < z < y.\)
