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Что (кто) такое infinite set - определение
SET WITH INFINITE CARDINALITY
Infinite sets; Infinite cardinality; Infinite (cardinality)
Найдено результатов: 2090
infinite set
<mathematics> A set with an infinite number of elements.
There are several possible definitions, e.g.
(i) ("Dedekind infinite") A set X is infinite if there exists
a bijection (one-to-one mapping) between X and some proper
subset of X.
(ii) A set X is infinite if there exists an injection from N
(the set of natural numbers) to X.
In the presence of the Axiom of Choice all such definitions
are equivalent.
(1995-03-27)
Infinite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
Dedekind-infinite set
PROPER SUBSET B OF A THAT IS EQUINUMEROUS TO A
Dedekind infinite; Dedekind-infinite; Dedekind finite; Dedekind finite set; Dedekind-finite set; Dedekind-finite; Dedekind infinity; Directly finite ring; Dedekind finite ring; Didekind infinite
In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A.
countably many
![The [[Cantor pairing function]] assigns one natural number to each pair of natural numbers](https://commons.wikimedia.org/wiki/Special:FilePath/Pairing natural.svg?width=200 "The [[Cantor pairing function]] assigns one natural number to each pair of natural numbers")
SET WITH THE SAME CARDINALITY AS THE SET OF NATURAL NUMBERS
Countably infinite; Countable sets; Countable; Countably; Denumerable; Countably many; Countability; Denumerability; Countably infinite set; Denumerable Set; Denumerably Infinite; Countable space; Countable infinity; Denumerable set; Countable infinite; Countable Set; Infinitely countable; Infinitely countable set; Listable infinity
Countable
SET WITH THE SAME CARDINALITY AS THE SET OF NATURAL NUMBERS
Countably infinite; Countable sets; Countable; Countably; Denumerable; Countably many; Countability; Denumerability; Countably infinite set; Denumerable Set; Denumerably Infinite; Countable space; Countable infinity; Denumerable set; Countable infinite; Countable Set; Infinitely countable; Infinitely countable set; Listable infinity
·adj Capable of being numbered.
denumerable
SET WITH THE SAME CARDINALITY AS THE SET OF NATURAL NUMBERS
Countably infinite; Countable sets; Countable; Countably; Denumerable; Countably many; Countability; Denumerability; Countably infinite set; Denumerable Set; Denumerably Infinite; Countable space; Countable infinity; Denumerable set; Countable infinite; Countable Set; Infinitely countable; Infinitely countable set; Listable infinity
[d?'nju:m(?)r?b(?)l]
¦ adjective Mathematics able to be counted by one-to-one correspondence with the set of integers.
Derivatives
denumerability noun
denumerably adverb
Origin
early 20th cent.: from late L. denumerare 'count out'.
countable
SET WITH THE SAME CARDINALITY AS THE SET OF NATURAL NUMBERS
Countably infinite; Countable sets; Countable; Countably; Denumerable; Countably many; Countability; Denumerability; Countably infinite set; Denumerable Set; Denumerably Infinite; Countable space; Countable infinity; Denumerable set; Countable infinite; Countable Set; Infinitely countable; Infinitely countable set; Listable infinity
<mathematics> A term describing a set which is isomorphic
to a subet of the natural numbers. A countable set has
"countably many" elements. If the isomorphism is stated
explicitly then the set is called "a counted set" or "an
enumeration".
Examples of countable sets are any finite set, the {natural
numbers}, integers, and rational numbers. The {real
numbers} and complex numbers are not [proof? ].
(1999-08-29)
Countable set
SET WITH THE SAME CARDINALITY AS THE SET OF NATURAL NUMBERS
Countably infinite; Countable sets; Countable; Countably; Denumerable; Countably many; Countability; Denumerability; Countably infinite set; Denumerable Set; Denumerably Infinite; Countable space; Countable infinity; Denumerable set; Countable infinite; Countable Set; Infinitely countable; Infinitely countable set; Listable infinity
In mathematics, a set is countable if it has the same cardinality (the number of elements of the set) as some subset of the set of natural numbers N = {0, 1, 2, 3, ...}.
infinite
2017 STUDIO ALBUM BY DEEP PURPLE
InFinite
1.
If you describe something as infinite, you are emphasizing that it is extremely great in amount or degree.
...an infinite variety of landscapes...
The choice is infinite.
ADJ [emphasis]
• infinitely
His design was infinitely better than anything I could have done.
ADV: ADV adj/adv
2.
Something that is infinite has no limit, end, or edge.
Obviously, no company has infinite resources.
ADJ
• infinitely
A centimeter can be infinitely divided into smaller units.
ADV: ADV with v
infinite
2017 STUDIO ALBUM BY DEEP PURPLE
InFinite
<mathematics> 1. Bigger than any natural number. There are
various formal set definitions in set theory: a set X is
infinite if
(i) There is a bijection between X and a proper subset of X.
(ii) There is an injection from the set N of natural numbers
to X.
(iii) There is an injection from each natural number n to X.
These definitions are not necessarily equivalent unless we
accept the Axiom of Choice.
2. The length of a line extended indefinitely.
See also infinite loop, infinite set.
[Jargon File ]
(1995-03-29)
Википедия
Infinite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
