User blog comment:P進大好きbot/Elementary Large Number/@comment-11227630-20190604040637/@comment-35470197-20190604045455

Exactly. That is what I intended by the canonical isomorphism \(\mathbb{Z}_2 \setminus \{0\} \cong \mathbb{N} \times (1 + 2 \mathbb{Z}_2)\) in the explanation above. By the way, I did not know that Loader's number uses the same method. It is interesting.