ordered pair
An object associated with a set of two objects considered in a particular order. Thus the ordered pair <a,b> is not identical with the ordered pair <b,a>, just as the queue ‘a first and b next’ is not the queue ‘b first and a next’. In set theory, ordered pairs cannot be identified with the set of their members, since a,b = b,a, which is exactly what we do not want. The task is to find sets with the property that <a,b> ? <b,a> if a ? b, and with the property that if <a,b> = <u,v> then a = u and b = v. One solution is that of Kazimierz Kuratowski (b. 1896), that identifies the ordered pair <a,b> with the set a,a,b. This is the definition in general use today. See also Cartesian product.

Philosophy dictionary. . 2011.

Look at other dictionaries:

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  • ordered pair — noun A set containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different set. Notation: (a, b) or See Also: triple, triplet, tuple …   Wiktionary

  • ordered pair — Math. two quantities written in such a way as to indicate that one quantity precedes or is to be considered before the other, as (3, 4) indicates the Cartesian coordinates of a point in the plane. [1950 55] …   Useful english dictionary

  • ordered pairs — ordered pair …   Philosophy dictionary

  • ordered — adj. 1. having or evincing a systematic arrangement; especially, having elements succeeding in order according to rule; as, an ordered sequence; an ordered pair. Opposite of {disordered} or {unordered}. [Narrower terms: {abecedarian,… …   The Collaborative International Dictionary of English

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  • Ordered vector space — A point x in R2 and the set of all y such that x≤y (in red). The order here is x≤y if and only if x1 ≤ y1 and x2 ≤ y2. In mathematics an ordered vector space or partially ordered vector space is a vector space equi …   Wikipedia

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