Question

Chứng tỏ rằng: nếu a,b ∈ Z và \(\left|a\right|\) < \(\left|b\right|\) thì -\(\left|b\right|\) < \(\left|a\right|\) <\(\left|b\right|\)

Giúp mk với

Answer 1

\(\left|a\right|< \left|b\right|\left(1\right)\Rightarrow-\left|a\right|>-\left|b\right|\left(2\right)\\ \left|a\right|\ge0\forall a; -\left|a\right|\le0\forall a\Rightarrow\left|a\right|\ge-\left|a\right|\left(3\right)\\ \text{Từ }\left(1\right),\left(2\right),\left(3\right)\Rightarrow-\left|b\right|< -\left|a\right|\le\left|a\right|< \left|b\right|\\ \Rightarrow-\left|b\right|< \left|a\right|< \left|b\right|\)