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The logarithm of an infinite cardinal number κ is defined as the least cardinal number μ such that κ ≤ 2 μ. Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of cardinal invariants of topological spaces , though they lack some of the properties that logarithms of positive real numbers possess.
In linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count. Examples in English are the words one , two , three , and the compounds three hundred [and] forty-two and nine hundred [and] sixty .
Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets.
In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa } is a regular cardinal if and only if every unbounded subset C ⊆ κ {\displaystyle C\subseteq \kappa } has cardinality κ {\displaystyle \kappa } .
Words in the cardinal category are cardinal numbers, such as the English one, two, three, which name the count of items in a sequence. The multiple category are adverbial numbers, like the English once , twice , thrice , that specify the number of events or instances of otherwise identical or similar items.
Pages in category "Cardinal numbers" The following 43 pages are in this category, out of 43 total. This list may not reflect recent changes. ...
aleph-nought, aleph-zero, or aleph-null) is the cardinality of the set of all natural numbers, and is an infinite cardinal.The set of all finite ordinals, called or (where is the lowercase Greek letter omega), also has cardinality .
Cardinal and Ordinal Numbers is a book on transfinite numbers, by Polish mathematician Wacław Sierpiński. It was published in 1958 by Państwowe Wydawnictwo Naukowe , as volume 34 of the series Monografie Matematyczne of the Institute of Mathematics of the Polish Academy of Sciences .