Infinite Family of Open Intervals disjoint, then The family must be numerable
i'm new on this. If we have a infinite family $\\{A_{\lambda}\\}_{\lambda\in\Lambda}$ of open intervals such $$A_{\lambda_1}\cap A_{\lambda_2}=\emptyset\;\;,\forall\lambda_1,\lambda_2\in\Lambda$$ then $\Lambda$ is numerable (biyection to $\mathbb{N}$)
Why?, I can't prove this and i'm feel bad for this