# ordered pair中的瑞典文-英文-瑞典文字典 格洛斯贝 - Glosbe

Ordnat par : definition of Ordnat par and synonyms of Ordnat

Here "initial segment" means a nonempty subset of $S$ closed under predecessors in the ordering. The above Kuratowski definition of the ordered pair is "adequate" in that it satisfies the characteristic property that an ordered pair must satisfy, namely that (,) = (,) ↔ (=) ∧ (=). In particular, it adequately expresses 'order', in that ( a , b ) = ( b , a ) {\displaystyle (a,b)=(b,a)} is false unless b = a {\displaystyle b=a} . 2011-07-14 · 2: the concept of a pairing scheme, as constructed, depends on the concept of a mapping. Typically, a mapping is constructed as a set of ordered pairs (which can be encoded as Kuratowski sets). Plainly, there is something flawed about an argument that depends on Kuratowski pairs to assert the unimportance of Kuratowski pairs.

Formalisations One may wish to declare ordered pairs to exist by fiat, which was done, for example, by both Bourbaki and Bill Lawvere . There are many mathematical definitions of ordered pair which have this property. The definition given here is the most common one: $(a,b) = \{\{a\}, \{a,b\}\}$. Kazimierz Kuratowski was the first person to make this definition.ru:Пара (математика)#Упорядоченная пара Answer to this is triple ordered pair.

you can use Kuratowski's set definition of ordered pair This page is based on the copyrighted Wikipedia article "Ordered_pair" ; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License. You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA.

## Ordnat par : definition of Ordnat par and synonyms of Ordnat

Since the behavior of Kuratowski  If relations are defined in terms of ordered pairs, this axiom requires a prior definition of ordered pair; the Kuratowski definition, adapted to ST, will do. 如果 关系以  Ordered Pairs, Products and Relations.

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{{x}, {x, y}}. “is less than” among numbers as the set of ordered pairs (m, n) of nat- ural numbers   Which ordered pair is on the graph of the equation 2x+5y=4?? Reply. An ordered pair contains the coordinates of one point in the coordinate system.

An ordered ordered pairs that we can create is called the set. (usually Kazimierz Kuratowski (1896-1980). Definition  relation can check if an object is the first (or second) projection of an ordered pair. Kuratowski pairs satisfy the characteristic property of ordered pairs: 〈a, b〉  One of the most cited versions of this definition is due to Kuratowski (see below) and his definition was used in the  Norbert Wiener, and independently Casimir Kuratowski, are usually credited with this discovery. A definition of 'ordered pair' held the key to the precise  The first of these orderings is called the ordered pair a, b, and number of ways to do this, but the most standard (published by Kuratowski (1921), modifying. Known as: Pair (mathematics), Kuratowski ordered pair, Kuratowski pair. Expand.
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Is (a,b) different from (a,a) when a=b? Next, what Cours netprof.fr de Mathématiques / DémonstrationProf : Jonathan It is an attempt to define ordered sets in terms of ordinary sets . We know that an n- tuple is different from the set of its coordinates. In an ordered set, the first element, second element, third element.. must be distinguished and identified. Definition of ordered pair in the Definitions.net dictionary.

Kazimierz Kuratowski was the first person to make this definition.ru:Пара (математика)#Упорядоченная пара This property is useful in the formal definition of an ordered pair, which is stated here but not explored in-depth. The currently accepted definition of an ordered pair was given by Kuratowski in 1921 (Enderton, 1977, pp. 36), though there exist several other definitions. Ordered pairs are also called 2-tuples, 2-dimensional vectors, or sequences of length 2. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another. An ordered pair is a pair of objects in which the order of the objects is significant and is used to distinguish the pair.

We would therefore add to the STLC $\zeta$ and $\cup$. The above Kuratowski definition of the ordered pair is "adequate" in that it satisfies the characteristic property that an ordered pair must satisfy, namely that . In particular, it adequately expresses 'order', in that is false unless . There are other definitions, of similar or lesser complexity, that are equally adequate: Ordered pairs are also called 2-tuples, 2-dimensional vectors, or sequences of length 2. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects).

and isn't { {a}, {a,a}, {a,a,a}} also same as {a} . So how to distinguish between (a,a) and (a,a,a) using Kuratowski definition? The above Kuratowski definition of the ordered pair is "adequate" in that it satisfies the characteristic property that an ordered pair must satisfy, namely that $${\displaystyle (a,b)=(x,y)\leftrightarrow (a=x)\land (b=y)}$$.
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Ladislav Mecir 14:17, 15 September 2016 (UTC) Unordered pairs. An introductory chapter of a mathematical monograph on most any topic may be devoted to elements of set theory. Or even a serious text on set theory may introduce an unordered pair as {a b}, where a b are the elements of the pair. Thus an unordered pair is simply a 1- or 2-element set.

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### Ordnat par : definition of Ordnat par and synonyms of Ordnat

It was the Polish mathematician Kazimierz Kuratowski who in 1921 came up with the definition that is now most commonly used: the one in which the ordered pair (a,b) is defined as the set {{a},{a,b}}. This definition, like the alternatives, has no deeper meaning other than that one can prove that the above property holds for it. Kuratowski's Definition of Ordered Pairs Thread starter gatztopher; Start date Aug 1, 2009; Prev.