n.可数性

The set of natural numbers is countable, meaning it is possible to put them in a one-to-one correspondence with the positive integers.
自然数集是可数的，这意味着可以将它们与正整数建立一一对应关系。
The rational numbers, though infinite, are also a countable set due to their ability to be listed systematically.
有理数虽然是无限的，但因为它们能够系统地列出，所以也是一个可数集。
Unlike the countable sets, the real numbers are uncountable; there's no way to create a complete list that includes every real number.
与可数集合不同，实数是不可数的；没有办法创建一个包含每个实数的完整列表。
The set of all finite strings composed of the letters in the English alphabet is countably infinite.
由英语字母表中的字母组成的所有有限字符串的集合是可数无限的。
Cantor's diagonal argument demonstrated that the set of all subsets of natural numbers is uncountable.
康托尔的对角线论证表明，所有自然数子集的集合是不可数的。
A countable union of countable sets is itself countable, illustrating the preservation of countability under union operations.
可数集合的可数并仍是可数的，这说明了在并集操作下可数性的保持。
The set of algebraic numbers, those that are roots of polynomial equations with integer coefficients, is countable.
代数数集，即整系数多项式方程的根，是可数的。
In set theory, a countable set is a set that has the same cardinality as the set of natural numbers, even if it's an infinite set.
在集合论中，一个可数集合是指与自然数集具有相同势（基数）的集合，即使它是无限的。
The set of all computer programs written in a given programming language is countable since each program can be represented by a finite string of characters.
使用给定编程语言编写的计算机程序的集合是可数的，因为每个程序都可以用有限长度的字符字符串表示。
Unlike finite sets, countably infinite sets cannot be put into a bijection with a subset of themselves that excludes just one element.
与有限集合不同，可数无限集合不能与自身的一个子集建立双射关系，该子集仅排除一个元素。