翻訳と辞書 Words near each other ・ Limingen ・ Limington ・ Limington Academy ・ Limington Historic District ・ Limington, Maine ・ Liminha ・ Limini ・ Liminka ・ Limit ・ Limit (category theory) ・ Limit (manga) ・ Limit (mathematics) ・ Limit (music) ・ Limit (roller coaster) ・ Limit analysis ・ Limit cardinal ・ Limit comparison test ・ Limit cycle ・ Limit dextrinase ・ Limit load ・ Limit load (aeronautics) ・ Limit load (physics) ・ Limit of a function ・ Limit of a sequence ・ Limit of positive stability ・ Limit of Vision ・ Limit or extend limits of debate ・ Limit ordinal ・ Limit point ・ Limit point compact Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Limit cardinal ： ウィキペディア英語版 Limit cardinal In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. These cardinals are sometimes called simply "limit cardinals" when the context is clear. A cardinal λ is a strong limit cardinal if λ cannot be reached by repeated powerset operations. This means that λ is nonzero and, for all κ < λ, 2κ < λ. Every strong limit cardinal is also a weak limit cardinal, because κ+ ≤ 2κ for every cardinal κ, where κ+ denotes the successor cardinal of κ. The first infinite cardinal, $\backslash aleph\_0$ (aleph-naught), is a strong limit cardinal, and hence also a weak limit cardinal. == Constructions == One way to construct limit cardinals is via the union operation: $\backslash aleph\_$ is a weak limit cardinal, defined as the union of all the alephs before it; and in general $\backslash aleph\_$ for any limit ordinal λ is a weak limit cardinal. The ב operation can be used to obtain strong limit cardinals. This operation is a map from ordinals to cardinals defined as :$\backslash beth\_\; =\; \backslash aleph\_0,$ :$\backslash beth\_\; =\; 2^\; =\; \backslash bigcup\; \backslash .$ The cardinal :$\backslash beth\_\; =\; \backslash bigcup\; \backslash ,\; \backslash beth\_,\; \backslash ldots\; \backslash \}\; =\; \backslash bigcup\_\; \backslash beth\_$ is a strong limit cardinal of cofinality ω. More generally, given any ordinal α, the cardinal :$\backslash beth\_\; =\; \backslash bigcup\_\; \backslash beth\_$ is a strong limit cardinal. Thus there are arbitrarily large strong limit cardinals. 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「Limit cardinal」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.