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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Additively indecomposable ordinal ： ウィキペディア英語版 Additively indecomposable ordinal In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any , we have The class of additively indecomposable ordinals (aka ''gamma numbers'') is sometimes denoted $\backslash mathbb.$ From the continuity of addition in its right argument, we get that if and α is additively indecomposable, then $\backslash beta\; +\; \backslash alpha\; =\; \backslash alpha.$ Obviously $1\backslash in\backslash mathbb$, since No finite ordinal other than $1$ is in $\backslash mathbb.$ Also, $\backslash omega\backslash in\backslash mathbb$, since the sum of two finite ordinals is still finite. More generally, every infinite cardinal is in $\backslash mathbb.$ $\backslash mathbb$ is closed and unbounded, so the enumerating function of $\backslash mathbb$ is normal. In fact, $f\_\backslash mathbb(\backslash alpha)=\backslash omega^\backslash alpha.$ The derivative $f\_\backslash mathbb^\backslash prime(\backslash alpha)$ (which enumerates fixed points of ''f''H) is written $\backslash epsilon\_\backslash alpha.$ Ordinals of this form (that is, fixed points of $f\_\backslash mathbb$) are called ''epsilon numbers''. The number $\backslash epsilon\_0=\backslash omega^\}$ is therefore the first fixed point of the sequence $\backslash omega,\backslash omega^\backslash omega\backslash !,\backslash omega^\backslash !\backslash !,\backslash ldots$ == Multiplicatively indecomposable == A similar notion can be defined for multiplication. The multiplicatively indecomposable ordinals (aka ''delta numbers'') are those of the form $\backslash omega^\; \backslash ,$ for any ordinal α. Every epsilon number is multiplicatively indecomposable; and every multiplicatively indecomposable ordinal is additively indecomposable. The delta numbers are the same as the prime ordinals that are limits. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Additively indecomposable ordinal」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.