Studiehandbok_del 3_200708 i PDF Manualzz
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This question hasn't been answered yet Ask an expert. this is triple ordered pair. you can use Kuratowski's set definition of ordered pair. Expert Answer . Previous question Next question Get more help from Chegg.
Kuratowski's definition. In 1921 Kazimierz Kuratowski offered the now-accepted definitioncf introduction to Wiener's paper in van Heijenoort 1967:224. van Heijenoort observes that the resulting set that represents the ordered pair "has a type higher by 2 than the elements (when they are of the same type)"; he offers references that show how, under certain circumstances, the type can be Kazimierz Kuratowski (Polish pronunciation: [kaˈʑimjɛʂ kuraˈtɔfskʲi]; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics . $\begingroup$ Now expressing the ordered pair as a set of sets according to the kuratowski definition, you will indeed have $(4,2) = \{\{4\},\{4,2\}\}$.
There are several equivalent ways but since you mention Kuratowski, his definition is "The ordered pair, (a, b), is the set {a, {ab}}. That's closest to your (2) but does NOT mean "a is a subset of b". "a" and "b" theselves are not necessarily sets at all.
Studiehandbok_del 3_200708 i PDF Manualzz
The history of the notion of "ordered pair" is not clear. As noted above, Frege (1879) proposed an intuitive ordering in his definition of a two-argument function Ψ(A, B). Pastebin.com is the number one paste tool since 2002. Pastebin is a website where you can store text online for a set period of time.
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Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2; ordered pairs of scalars are also called 2-dimensional vectors. In classical Euclidean geometry (that is in synthetic geometry), vectors were introduced (during 19th century) as equivalence classes, under equipollence, of ordered pairs of points; two pairs Therefore [latex]x = u[/latex] and [latex]y = v[/latex]. 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.
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A×B, is the set of all ordered pairs
Ordered pairs of scalars are sometimes called 2-dimensional vectors. (Technically, this is an abuse of notation since an ordered pair need not be an element of a vector space.) The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). Ordered pairs are necessary in defining the Cartesian Product, which in turn are used to define relations, functions, coordinates, etc. Mathematical Structures Tuples are often used to encapsulate sets along with some operator or relation into a complete mathematical structure. 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).
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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.
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.
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Studiehandbok_del 3_200708 i PDF Manualzz
Now consider an ordered triplet (a,a,a) it would be defined as { {a}, {a,a}, {a,a,a}}. 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 \({\displaystyle (a,b)=(x,y)\leftrightarrow (a=x)\land (b=y)}\).
ordered pair中的瑞典文-英文-瑞典文字典 格洛斯贝 - Glosbe
{{x}, {x, y}}.
$\begingroup$ Now expressing the ordered pair as a set of sets according to the kuratowski definition, you will indeed have $(4,2) = \{\{4\},\{4,2\}\}$. On the left that is an ordered pair, the second element of which is $2$. The concept of Kuratowski pair is one possible way of encoding the concept of an ordered pair in material set theory (say in the construction of Cartesian products ): A pair of the form. ( a, b) (a,b) is represented by the set of the form.