Примери коришћења Cardinal number на Енглеском и њихови преводи на Српски
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The cardinal number fifty.
The first six cardinal numbers.
There are two approaches to cardinality- one which compares sets directly using bijections and injections,and another which uses cardinal numbers.
C is for cardinal numbers.
Which is the smallest countably infinite cardinal number.
All other cardinal numbers are indeclinable!
The Addition of Infinite Cardinal Numbers.
How to convert cardinal number to ordinal number in Excel?
Is the smallest uncountable cardinal number.
Many people get cardinal numbers and ordinal numbers confused.
The contrast of this is a cardinal number.
Aleph-ω is the first uncountable cardinal number that can be demonstrated within Zermelo-Fraenkel set theory not to be equal to the cardinality of the set of all real numbers; .
Aleph-naught, the smallest infinite cardinal number.
Cantor's problem of the cardinal number of the continuum.
Aleph-naught, or aleph-null, the smallest infinite cardinal number.
Natural numbers- count the elements of a whole, cardinal number or express the order which occupies an element.
The definition of implies(in ZF, Zermelo-Fraenkel set theory without the axiom of choice) that no cardinal number is between and.
In 1899 Cantor had himself posed the question"What is the cardinal number of the set of all sets?", and obtained a related paradox.
There are two approaches to cardinality – one which compares sets directly using bijections, injections, and surjections,and another which uses cardinal numbers….
For ordinals greater than tenth, cardinal numbers are used.
Indeed, in axiomatic set theory, this is taken as the definition of"same number of elements", andgeneralising this definition to infinite sets leads to the concept of cardinal number.
Note: For ordinal numbers greater than 10, cardinal numbers are used instead.
Continuing in this manner, it is possible to define a cardinal number ℵ α{\displaystyle\aleph_{\alpha}} for every ordinal number α.
To define for arbitrary ordinal number α,we must define the successor cardinal operation, which assigns to any cardinal number ρ the next bigger well-ordered cardinal ρ+.
If the axiom of choice(AC) is used, it can be further proved that the class of cardinal numbers is totally ordered, andthus is the second-smallest infinite cardinal number.
Indeed, in axiomatic set theory, this is taken as the very definition of"same number of elements", andgeneralising this definition to infinite sets leads to the concept of cardinal number, a way to distinguish the various sizes of infinite sets.
Conventionally the smallest infinite ordinal is denoted ω,and the cardinal number ℵ ω{\displaystyle\aleph_{\omega}} is the least upper bound of.
In 1899 Cantor had himself posed the question:"what is the cardinal number of the set of all sets?
For an infinite graph G, one may define the coloring number analogously to the definition for finite graphs,as the smallest cardinal number α such that there exists a well-ordering of the vertices of G in which each vertex has fewer than α neighbors that are earlier in the ordering.
The definition of ℵ 1{\displaystyle\aleph_{1}} implies(in ZF, Zermelo-Fraenkel set theory without the axiom of choice)that no cardinal number is between ℵ 0{\displaystyle\aleph_{0}} and ℵ 1{\displaystyle\aleph_{1}}.