Dense order

Dense order

In mathematics, a partial order or total order < on a set is said to be dense if, for all and in for which , there is a in such that . That is, for any two elements, one less than the other, there is another element between them. For total orders we can say this more simply as "for any two distinct elements, there is another element between them", since totality implies that two distinct elements are related by , but this is false in general for partial orders because distinct elements can be incomparable.
http://dbpedia.org/resource/Dense_order
Dense_order
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Dense order

In mathematics, a partial order or total order < on a set is said to be dense if, for all and in for which , there is a in such that . That is, for any two elements, one less than the other, there is another element between them. For total orders we can say this more simply as "for any two distinct elements, there is another element between them", since totality implies that two distinct elements are related by , but this is false in general for partial orders because distinct elements can be incomparable.
http://dbpedia.org/resource/Dense_order
has abstract
Dichte Ordnung ist ein mathema ...... i Elementen ein drittes liegt.
@de
En matemática, y particularmen ...... al en los enteros no es densa.
@es
Husté uspořádání je matematick ...... ém uspořádání podle velikosti.
@cs
In mathematics, a partial orde ...... elements can be incomparable.
@en
In teoria degli ordini, una br ...... , cioè tale che per ogni x, y:
@it
La notion d'ordre dense est un ...... la notion de relation d'ordre.
@fr
Плотный порядок — это отношени ...... к плотного порядка бесконечен.
@ru
数学における稠密関係（ちゅうみつかんけい、英: dense ...... 方、整数全体の成す集合に通常の順序を入れたものは稠密でない。
@ja
순서론에서 조밀 순서(稠密順序, 영어: dense order)는 서로 다른 두 비교 가능 원소 사이에 항상 제3의 원소가 존재하는 부분 순서이다.
@ko
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@en
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For the element , due to the A ...... , and . Therefore is dense.
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Proof
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Dichte Ordnung ist ein mathema ...... i Elementen ein drittes liegt.
@de
En matemática, y particularmen ...... al en los enteros no es densa.
@es
Husté uspořádání je matematick ...... ém uspořádání podle velikosti.
@cs
In mathematics, a partial orde ...... elements can be incomparable.
@en
In teoria degli ordini, una br ...... , cioè tale che per ogni x, y:
@it
La notion d'ordre dense est un ...... la notion de relation d'ordre.
@fr
Плотный порядок — это отношени ...... к плотного порядка бесконечен.
@ru
数学における稠密関係（ちゅうみつかんけい、英: dense ...... 方、整数全体の成す集合に通常の順序を入れたものは稠密でない。
@ja
순서론에서 조밀 순서(稠密順序, 영어: dense order)는 서로 다른 두 비교 가능 원소 사이에 항상 제3의 원소가 존재하는 부분 순서이다.
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label
Dense order
@en
Dichte Ordnung
@de
Husté uspořádání
@cs
Orden denso
@es
Ordine denso
@it
Ordre dense
@fr
Плотный порядок
@ru
稠密関係
@ja
조밀 순서
@ko
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