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See all on Wikipediahttps://en.wikipedia.org/wiki/Ordered_pairIn mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.) Ordered pairs are also called 2-tuples, or … See more
Let $${\displaystyle (a_{1},b_{1})}$$ and $${\displaystyle (a_{2},b_{2})}$$ be ordered pairs. Then the characteristic (or defining) property of the ordered pair is:
The See moreA category-theoretic product A × B in a category of sets represents the set of ordered pairs, with the first element coming from A and the second coming from B. In this … See more
In some introductory mathematics textbooks an informal (or intuitive) definition of ordered pair is given, such as
For any two objects a and b, the ordered pair (a, b) is a … See moreIf one agrees that set theory is an appealing foundation of mathematics, then all mathematical objects must be defined as sets of some sort. Hence if the ordered pair is not taken as … See more
• Cartesian product
• Tarski–Grothendieck set theory
• Trybulec, Andrzej, 1989, "Tarski–Grothendieck Set Theory", Journal of Formalized Mathematics (definition Def5 of "ordered pairs" as { { x,y }, { x } }) See moreWikipedia text under CC-BY-SA license- https://simple.wikipedia.org/wiki/Ordered_pair
In mathematics, an ordered pair is a collection of two objects, where one of the objects is first (the first coordinate or left projection ), and the other is second (the second coordinate or right …
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- https://en.wikipedia.org/wiki/Cartesian_product
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation, that is
A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the for…Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 4 mins
- https://en.wikipedia.org/wiki/Tuple
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For …
- https://en.wikipedia.org/wiki/Directed_graph
A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A ), arrows, or directed lines. It differs from an …
- https://en.wikipedia.org/wiki/Unordered_pair
While the two elements of an ordered pair (a, b) need not be distinct, modern authors only call {a, b} an unordered pair if a ≠ b. But for a few authors a singleton is also considered an …
- https://math.stackexchange.com/questions/62908
For a metaphor: the ordered pair is like a car; we know how to drive. But in order to actually have a car, there needs to be an engine and gasoline, and the engine has to work. We are trying to …
- https://en.wiktionary.org/wiki/ordered_pair
Noun [ edit] ordered pair ( plural ordered pairs ) ( set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a …
- https://en.wikipedia.org/wiki/Pair
Ordered pair, in mathematics and set theory. Pairing, in mathematics, an R-bilinear map of modules, where R is the underlying ring. Pair type, in programming languages and type theory, …
- https://en.wikipedia.org/wiki/Axiom_of_pairing
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory. It was introduced by …
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