###### tags: `108上助教` `數學`
# 數學導論HW10
## ch7-7


#### **proof**

Let $A$ be a countable set
then $|A| = \aleph_0$
and select $a_1 , a_2 , \ldots , a_{n} \in A$
let $B = \{a_1 , a_2 , \ldots , a_{n}\}$
$\Rightarrow |B| = n$

By definition,
$\aleph_0 + n = |A| + |B| = |A \cup B| = |A| = \aleph_o\ \Box$