Set theory | Cardinal numbers

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, (aleph-naught), is a strong limit cardinal, and hence also a weak limit cardinal. (Wikipedia).

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From playlist Limits

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From playlist Limits

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From playlist Limits

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From playlist CALCULUS 1 CH 1 LIMITS & DERIVATIVES

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Calculus 1: Limits & Derivatives (13 of 27) Limits and Horizontal Asymptotes

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From playlist CALCULUS 1 CH 1 LIMITS & DERIVATIVES

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Dima Sinapova : Prikry type forcing and combinatorial properties

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Related pages

Successor cardinal | Zermelo–Fraenkel set theory | Large cardinal | Regular cardinal | Cardinal number | Limit ordinal | Mathematics | Inaccessible cardinal | Power set | Aleph number | Beth number | Cofinality