게으른맽랩 lazy matlab

Suppose a set $X = \{x_{\alpha} > 0 | \alpha \in I\}$ is an uncountable set. We will show that the sum of all elements of $X$ is infinite. Consider the family of the following sets.  $$S_n := \left\{ x_{\alpha} \in X \; \mid \; x_{\alpha} \ge \frac{1}{n} \right\}$$  Then  $$\bigcup_{n\in \mathbb{N}} S_n = X$$  $X$ is uncountable, so there exists $n_0 \in \mathbb{N}$ such that $S_{n_0}$ is an infin..