tag:blogger.com,1999:blog-2237906900456925233.post7953298220970511476..comments2023-10-18T23:36:58.396+08:00Comments on 數學資料庫手記: 選擇公理MathDBhttp://www.blogger.com/profile/18353093974880979999noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2237906900456925233.post-41370671210410424262008-03-23T21:22:00.000+08:002008-03-23T21:22:00.000+08:00“選擇公理” 想得多真的會令人發癲,Jerry Bona的話實在合理得太容易令人相信"The Axi...“選擇公理” 想得多真的會令人發癲,Jerry Bona的話實在合理得太容易令人相信<BR/>"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" <BR/>第三個例子很有趣,期待著你的答案!Singmayhttps://www.blogger.com/profile/10355377961945631283noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-81759114557471607232008-03-21T14:05:00.000+08:002008-03-21T14:05:00.000+08:00可否這樣看?AC 其實在 N 的範圍內是可以用 ZC 證的,即[wiki]Not every sit...可否這樣看?<BR/>AC 其實在 N 的範圍內是可以用 ZC 證的,即<BR/><I>[wiki]Not every situation requires the axiom of choice. For finite sets X, the axiom of choice follows from the other axioms of set theory. In that case it is equivalent to saying that if we have several (a finite number of) boxes, each containing at least one item, then we can choose exactly one item from each box.[/wiki]</I>Anonymoushttps://www.blogger.com/profile/03145671850453012223noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-27455000759495400292008-03-21T04:05:00.000+08:002008-03-21T04:05:00.000+08:00我的想法是,這些paradox應該不會和已有的東西有矛盾(否則我們可以透過其他公理去反證它,這和AC...我的想法是,這些paradox應該不會和已有的東西有矛盾(否則我們可以透過其他公理去反證它,這和AC與ZF獨立的事實矛盾!),而只是和我們的「常理」矛盾,所以不見得有問題。<BR/> 事實上,量子力學本身極大部份都是和「常理」矛盾,但當中有一部份已經為實驗證實,至少,你我所用的電腦或多或少都是量子力學的產品。ychjaehttps://www.blogger.com/profile/01050435897743924997noreply@blogger.comtag:blogger.com,1999:blog-2237906900456925233.post-84697999009586288642008-03-21T00:00:00.000+08:002008-03-21T00:00:00.000+08:00補充一下,axiom of choice 其實在很多範疇也需要應用,如Banach algebra,...補充一下,axiom of choice 其實在很多範疇也需要應用,如Banach algebra,而這些algebra得出的結果正是某些量子力學理論的根基...<BR/><BR/>如果axiom of choice有Banach-Tarski 等 Paradox 的出現,數學家絕對有必要釐清其歧義,否則量子力學的理論基礎也岌岌可危。<BR/><BR/>(我好像踏過界了,如有錯誤請賜教)Danhttps://www.blogger.com/profile/12622915842475953726noreply@blogger.com