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:
“Can you find out the deep things of God? Can you find out the limit of the Almighty?”
—Bible: Hebrew, Job 11:7.
“To this war of every man against every man, this also is consequent; that nothing can be Unjust. The notions of Right and Wrong, Justice and Injustice have there no place. Where there is no common Power, there is no Law; where no Law, no Injustice. Force, and Fraud, are in war the two Cardinal virtues.”
—Thomas Hobbes (1579–1688)