Ordinal Numbers

[ZFC Set Theory] Appendix B. 서수 Ordinal NumbersBy 초코맛 도비

[lang-en]This post deals with random things related with ordinal numbers, which were not covered in the series posts. One day, this post might be quite long. No one knows for sure. :-)[/lang-en] [lang-ko]이 포스트는 공리적 집합론과 관련이 있으나 시리즈 글들에서 다루지 못한 내용들을 다루는 글입니다. 언젠가는 글이 상당히 길어질지도 모르죠. 확실한 건 아무도 모릅니다. :-)[/lang-ko] i. [lang-ko]시리즈 글들[/lang-ko][lang-en]List of Series Posts[/lang-en] VI. 전순서 집합 Well-Or..

[ZFC Set Theory] VII. 서수 Ordinal NumbersBy 초코맛 도비

[lang-en]To see the previous post[/lang-en][lang-ko]이전 글 보러가기[/lang-ko] $\def\Ord{\operatorname{Ord}}$ [lang-en]In this post, as commented on the previous post, we shall give a formal definition of ordinal numbers, which are order-types of well-ordered sets. When considering Theorem VI.6, it is natural to think that the order-type of $W_1$ is less than the order-type of $W_2$ if and only if $W_1..