Inter-universal geometry と ABC予想 (応援スレ) 64at MATHInter-universal geometry と ABC予想 (応援スレ) 64 - 暇つぶし2ch■コピペモード□スレを通常表示□オプションモード□このｽﾚｯﾄﾞのURL■項目テキスト650:first. Writing 0' < 1' < 2' < ... for the second copy, ω + ω looks like 0 < 1 < 2 < 3 < ... < 0' < 1' < 2' < ... This is different from ω because in ω only 0 does not have a direct predecessor while in ω + ω the two elements 0 and 0' do not have direct predecessors. Multiplication Here is ω・2: 00 < 10 < 20 < 30 < ... < 01 < 11 < 21 < 31 < ..., which has the same order type as ω + ω. Exponentiation For instance, ω^2 = ω・ω using the operation of ordinal multiplication. Note that ω・ω can be defined using the set of functions from 2 = {0,1} to ω = {0,1,2,...}, ordered lexicographically with the least significant position first: (0,0) < (1,0) < (2,0) < (3,0) < ... < (0,1) < (1,1) < (2,1) < (3,1) < ... < (0,2) < (1,2) < (2,2) < ... Here for brevity, we have replaced the function {(0,k), (1,m)} by the ordered pair (k, m). (引用終り) 以上 次ページ最新レス表示レスジャンプ類似スレ一覧スレッドの検索話題のニュースおまかせリストオプションしおりを挟むスレッドに書込スレッドの一覧暇つぶし2ch