1. The set of all prime numbers is countably infinite.
所有质数的集合是可数无限的。

2. The integers are countably infinite because they can be listed in a sequence.
整数是可数无限的，因为它们可以按顺序列出。

3. The set of rational numbers is countably infinite, as each rational number can be mapped to a unique integer.
有理数集是可数无限的，因为每个有理数可以映射到一个唯一的整数。

4. The set of even numbers is countably infinite, as they can be paired with the integers.
偶数集是可数无限的，因为它们可以与整数配对。

5. The set of natural numbers is countably infinite, as they can be listed in a one-to-one correspondence with the integers.
自然数集是可数无限的，因为它们可以与整数一一对应。

6. A countably infinite set can be put in a one-to-one correspondence with the set of natural numbers.
可数无限集合可以与自然数集一一对应。