# 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

### Famous quotes containing the words limit and/or cardinal:

An educational method that shall have liberty as its basis must intervene to help the child to a conquest of liberty. That is to say, his training must be such as shall help him to diminish as much as possible the social bonds which limit his activity.
Maria Montessori (1870–1952)

The Cardinal is at his wit’s end—it is true that he had not far to go.
George Gordon Noel Byron (1788–1824)