[tex]\left \lfloor x \right \rfloor\left \{ x \right \} < x-1\Leftrightarrow \lfloor x\rfloor\{x\} < \lfloor x\rfloor+\{x\}-1\Leftrightarrow (\lfloor x\rfloor-1)(\{x\}-1) < 0\Rightarrow\\\Rightarrow \lfloor x\rfloor > 1\Rightarrow x\geq 2[/tex]