Countable infinity

Japanese: 可算無限 - かさんむげん

...In that case, we can define it as "a set that has a one-to-one correspondence with all natural numbers is called a countable set, and the cardinality of that set is called countable." To make it clear that it is an infinite set, it is sometimes called countably infinite. For example, the whole set of integers is countably infinite because we can assign numbers to them as shown in Figure 1.

From [Gathering]

...〈For any set M , ^{2♯( M )} ＞♯( M )〉(diagonal argument).
[Countable infinity and the density of the continuum]
The smallest cardinality of infinity is the cardinality of the set N of all natural numbers. This is called the cardinality of countable infinity (or numberable infinity).

*Some of the terminology explanations that mention "countable infinity" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…その場合は〈自然数の全体と1対1の対応をする集合を可算集合といい，その集合の濃度を可算という〉と定義すればよい。無限集合であることをはっきりさせるために可算無限ということもある。例えば整数全体は，図1のように番号をつけていくことができるので可算無限である。…