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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, (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: is a weak limit cardinal, defined as the union of all the alephs before it; and in general 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 : : The cardinal : is a strong limit cardinal of cofinality ω. More generally, given any ordinal α, the cardinal : 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
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