Generally, you must assume well-ordering to prove the principle of transfinite induction (they are equivalent). Induction should not be taken for granted; there are sets where induction does not hold!
_________________ If I have seen farther, it is by standing on the shoulders of the giants.---Newton
2007-02-01 19:58
isomorphism Not too shy to talk
註冊日: 2007-01-30 發表數: 40
Re: 要如何證明數學歸納法...
I question the validity of this proof. I think it is a mere restatement of the conditions of induction.
Usually, a proof of induction on the natural numbers first considers the set of all members such that P(a) is false, and considers the least element of that set.
2007-02-01 21:56
孫文先 Moderator
註冊日: 2002-07-30 發表數: 1094
Re: 要如何證明數學歸納法...
亦可參考《數學歸納法縱橫談》九章出版
_________________ 孫文先 敬上
2007-02-02 09:13
九章數學出版社、九章數學基金會版權所有 本網頁各鍊結標題及鍊結內容歸原權利人所有 Copyright 2000 ~2004九章數學出版社、九章數學基金會 本網站內所有文字及資料版權均屬九章所有,未經書面同意之商業用途必究 This web site was made with XOOPS, a web portal system written in PHP. XOOPS is a free software released under the GNU/GPL license.