Let $a, b, \lambda \in \mathbb{R}$ each be a D993: Real number such that
(i) | \begin{equation} a \leq b \end{equation} |
(ii) | \begin{equation} \lambda \in (0, \infty) \end{equation} |
Then
(1) | \begin{equation} \lambda (a, b) = (\lambda a, \lambda b) \end{equation} |
(2) | \begin{equation} \lambda [a, b) = [\lambda a, \lambda b) \end{equation} |
(3) | \begin{equation} \lambda (a, b] = (\lambda a, \lambda b] \end{equation} |
(4) | \begin{equation} \lambda [a, b] = [\lambda a, \lambda b] \end{equation} |