English Dictionary

countably infinite

形容詞

比較不可 集合

(set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.

日本語の意味

可算無限：数え上げ可能な無限集合、すなわち自然数全体と同じ濃度（カーディナリティ）を持つ集合 / 自然数集合 ℕ と一対一に対応可能な無限集合 / 順序を付けて数えることができる無限集合

The mathematician explained that the set of all prime numbers is countably infinite, even though its pattern is not fully understood.

その数学者は、すべての素数の集合が可算かつ無限であると説明したが、その分布の法則は完全には解明されていない。

意味（1）

(set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.

This one-to-one correspondence between the set of positive integers and the set of pairs of positive integers indicates that the set of pairs is countably infinite. Since the set of positive rational numbers is a subset of the set of all pairs of positive integers, the set of positive rational numbers is at most countably infinite. Then, since it is also at least countably infinite, the set of positive rational numbers is countably infinite.