Limit Cardinal

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 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.

Read more about Limit Cardinal:  Constructions, Relationship With Ordinal Subscripts, The Notion of Inaccessibility and Large Cardinals

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