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cardinalnumber

cardinal number

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The answer CARDINALNUMBER (cardinal number) has 9 possible clue(s) in existing crosswords.

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Definitions of cardinal number in various dictionaries:

noun - the number of elements in a mathematical set

CARDINAL NUMBER - That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures.

CARDINAL NUMBER - In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets....

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Possible Crossword Clues
Murder: cannibal is suspect, for one, among others
Maybe one church dignitary's less sensitive
One is the first churchman with less feeling
One who teaches math at the Vatican?
Red, indigo's second, then brown one, perhaps?
Aviary anesthetist?
Brutal murder, cannibal producing one, perhaps
For instance, one clergyman's more stupefied
It could be one songbird with a musical item

Cardinal number might refer to
In mathematics, Cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets. * Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set, something that cannot happen with proper subsets of finite sets. * There is a transfinite sequence of cardinal numbers:* * * * 0 * , * 1 * , * 2 * , * 3 * , * … * , * n * , * … * ; * * ℵ * * 0 * * * , * * ℵ * * 1 * * * , * * ℵ * * 2 * * * , * … * , * * ℵ * * α * * * , * … * . * * * * {\displaystyle 0,1,2,3,\ldots ,n,\ldots ;\aleph _{0},\aleph _{1},\aleph _{2},\ldots ,\aleph _{\alpha },\ldots .\ } * This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers (infinite cardinals of well-ordered sets). The aleph numbers are indexed by ordinal numbers. Under the assumption of the axiom of choice, this transfinite sequence includes every cardinal number. If one rejects that axiom, the situation is more complicated, with additional infinite cardinals that are not alephs. * Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra, and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.

Cardinal number might refer to

In mathematics, Cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets.
* Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set, something that cannot happen with proper subsets of finite sets.
* There is a transfinite sequence of cardinal numbers:*
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* {\displaystyle 0,1,2,3,\ldots ,n,\ldots ;\aleph _{0},\aleph _{1},\aleph _{2},\ldots ,\aleph _{\alpha },\ldots .\ }
* This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers (infinite cardinals of well-ordered sets). The aleph numbers are indexed by ordinal numbers. Under the assumption of the axiom of choice, this transfinite sequence includes every cardinal number. If one rejects that axiom, the situation is more complicated, with additional infinite cardinals that are not alephs.
* Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra, and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.

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