>>142-144
>整列可能定理と選択公理の関係から、両者に「可算」を付けても同じだろうと
>連想したのだろうが、証明を読めば事情はまったく異なる。

やれやれ
証明が読めてない人は、だれでしょか？ ；ｐ）
下記に、整列可能定理→選択公理 の証明を、貼ります！
英語版が分りにくいので、中国版とイタリア版 を追加した
百回音読してね

(参考)
en.wikipedia.org/wiki/Well-ordering_theorem
Well-ordering theorem
Proof of axiom of choice
The axiom of choice can be proven from the well-ordering theorem as follows.
To make a choice function for a collection of non-empty sets,
E, take the union of the sets in
E and call it X.
There exists a well-ordering of
X; let R be such an ordering. The function that to each set S of E
associates the smallest element of S, as ordered by (the restriction to S of) R, is a choice function for the collection E.■
An essential point of this proof is that it involves only a single arbitrary choice, that of
R; applying the well-ordering theorem to each member S of E separately would not work, since the theorem only asserts the existence of a well-ordering, and choosing for each S a well-ordering would require just as many choices as simply choosing an element from each S.

つづく