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Topic: Ordered pair

	Ordered pair
		An ordered pair is a collection of two objects such that one can be distinguished as the first element and the other as the second element.
		An ordered pair with first element a and second element b is usually written as (a, b).
		Ordered triples and n-tuples (ordered lists of n terms) are defined recursively from this definition: an ordered triple (a,b,c) can be defined as (a, (b,c)): two nested pairs.
	www.ebroadcast.com.au /lookup/encyclopedia/or/Ordered_pair.html (362 words)

	PlanetMath: ordered pair
		The characterizing property of an ordered pair is:
		and the above construction of ordered pair, as weird as it seems, is actually the simplest possible formulation which achieves this property.
		This is version 4 of ordered pair, born on 2001-10-19, modified 2002-03-04.
	planetmath.org /encyclopedia/OrderedPair.html (91 words)

	Ordered pair - Wikipedia, the free encyclopedia
		In mathematics, an ordered pair is a collection of two objects such that one can be distinguished as the first element and the other as the second element (the first and second elements are also known as left and right projections).
		An ordered pair with first element a and second element b is often written as (a, b).
		In type theory, and in set theories such as New Foundations that are outgrowths of type theory, this pair is of the same type as its projections (and hence is termed a "type-level" ordered pair).
	en.wikipedia.org /wiki/Ordered_pair (927 words)

	Cooper Pairs and the BCS Theory of Superconductivity
		The behavior of superconductors suggests that electron pairs are coupling over a range of hundreds of nanometers, three orders of magnitude larger than the lattice spacing.
		This pair condensation is the basis for the BCS theory of superconductivity.
		The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.
	hyperphysics.phy-astr.gsu.edu /hbase/solids/coop.html (509 words)

	Lesson 1
		The ordered pair for the corral is (D,1).
		In math ordered pairs are often used to describe locations and to record scientific data.
		It can be described by a set of ordered pairs, C = { (-2,4), (-2,1), (0,-3), (3,-1)}, which gives the coordinates of the points of the graph.
	www.dis.dpi.state.nd.us /ISC/classes/example/Alg2/L1.html (1418 words)

	Binary Relation
		Relation, a mathematical concept, is a set of ordered pairs.
		One interprets a relation as a relationship (in the quotidian parlance) from the first coordinate to the second coordinate of the ordered pair.
		Consequently, every element in I is an ordered pair that has the same first and second component and every element in X forms such an ordered pair in I. In symbols, I = {(x, x) : for all x in X}.
	www.iscid.org /encyclopedia/Binary_Relation (2105 words)

	Graphing Games for Hands-On Math, Fran Endicott Armstrong, Ph.D., SLCC/MC (Site not responding. Last check: 2007-11-04)
		Don't forget to include among the ordered pairs ones that have 0 as the first component (no sideways movement, so the point is on the vertical axis) and 0 as the second component (no vertical movement, so the point is on the horizontal axis).
		That is, either the Hider corrects the ordered pair written on the board and announces the corrected location of the object or the Seeker uses the information provided by the ordered pair to correctly locate the node at which the object is hidden.
		Then the Seeker goes to the location indicated by the ordered pair, finds the object, and returns the object to the container of objects (or keeps the object if the teacher is giving the objects away this day).
	www.stlcc.cc.mo.us /mc/dept/math/homl/grphgame.htm (1563 words)

	Definition of Relation
		The order of the objects must also be taken into account, because John owns a red Mustang but the red Mustang does not own John, and simple sets do not deal with orders.
		from a set A to a set B is a set of ordered pairs where a is an element of A and b is an element of B.
		The set of all ordered pairs , where a is an element of A and b is an element of B, is called the
	www.cs.odu.edu /~toida/nerzic/content/relation/definition/definition.html (470 words)

	Pairs figure skating photos, Ice Skating Pictures by Tracy Marks, Olympic and World Championships Figure Skaters
		Pairs skating involves a woman and man performing single figure skating moves (such as step sequences, jumps and spins) side by side and in unison AND specific pairs movements.
		In figure skating shows, pairs skaters may perform dramatic and dangerous moves which which are banned at the Olympics, Worlds, U.S. Nationals and other competitions - such as the headbanger (the man swinging the woman by her legs) or the Detroiter (man lifting her by her legs while spinning).
		In order to sit close to the ice, I try to buy my tickets as early as possible, but often end up in the 10th row or further back and have to rely on a 300zoom lens to get closeup pictures.
	www.webwinds.com /pairs/pairs.htm (425 words)

	Letter-pairs analysis (Site not responding. Last check: 2007-11-04)
		This project consists in a programming application that is able to read a text and to calculate in real time the number of times each pair of letters appears in a given text.
		For each new given pair of letters found in the text, the program generates a new bubble.
		The final output result of this algorithm allows you to have a fast and comprehensive vision of which are the pairs of letters more used in certain text and language.
	www.m-i-b.com.ar /mib/letter_pairs/eng (260 words)

	Title: Hit the Slopes
		-An ordered pair of numbers identifies the locations of a point; these numbers are the coordinates of the point on the graph.
		We represent an ordered pair of numbers symbolically by placing the numbers inside parentheses and separating them with a comma.
		Ask each pair of students to provide answers and explain how they arrived at those answers, without telling them if they are correct or not.
	www.auburn.edu /~cotneml/lessonplantwo.htm (1428 words)

	3
		These ordered pairs contain the corresponding x and y-values that make the equation a true statement.
		When the solutions of these equations, the ordered pairs, are graphed, these points form a straight line.
		As you move the cursor on the line using the left or right arrows, the x and y coordinates of each point are displayed at the bottom of the graph.
	mtsu32.mtsu.edu:11237 /chp3,section2.htm (454 words)

	New Page 1
		Remember, an ordered pair is always written with the x value first and the y value second, following alphabetical order: (x, y).
		We generally find three ordered pairs that are solutions in order to find the correct straight line.
		This happens because there is an infinite number of ordered pairs that are solutions of this equation.
	www.lcsc.edu /ahanson/Lessons/Lesson16.htm (940 words)

	"Removable Pair Conjecture" (Site not responding. Last check: 2007-11-04)
		Definitions: A removable pair of elements in a partially ordered set P is a pair {x,y} such that removing x and y does not drop the dimension of the poset by more than one.
		A minimal element and maximal element that are incomparable form a removable pair.
		Trotter and Bogart [TB1] posed a stronger conjecture that every unforced pair is a removable pair, but Reuter [R] found a counterexample in dimension 4.
	www.math.uiuc.edu /~west/openp/rempair.html (395 words)

	Set Theory > Basic Set Theory (Stanford Encyclopedia of Philosophy)
		For many applications, we need to pair a and b in a way making possible to “read off” which set comes “first” and which comes “second.” We denote this ordered pair of a and b by (a, b); a is the first coordinate of the pair (a, b), b is the second coordinate.
		It should be defined in such a way that two ordered pairs are equal if and only if their first coordinates are equal and their second coordinates are equal.
		A binary relation is determined by specifying all ordered pairs of objects in that relation; it does not matter by what property the set of these ordered pairs is described.
	plato.stanford.edu /entries/set-theory/primer.html (2793 words)

	[No title]
		Draw a line through the columns of any other ordered pairs in R where the first element is equal to the second element of the first ordered pair.
		Where the lines intersect, the ordered pairs must all be in R, for the relation to be transitive.
		When these four conditions hold, then relation R is a PARTIAL ORDERING of set S. It defines ordered pairs for part of the elements of set S, but not all of them.
	www.unf.edu /public/cot3100/jgiles/lecture5 (1387 words)

	ordered pair (Site not responding. Last check: 2007-11-04)
		However, a tuple in database theory is usually defined as a finite function that maps fields in a relation(database table for instance) to data, and is not necessarily an ordered set of n elements.
		then the ordered pair (a,b) is a function f with f(1) = a and f(2) = b, so there are two "copies" of a, one taken first and one taken second.
		to say that when both elements of the pair are equal, one does not need to designate one as first is different from saying there are two elements, one first one second, and both are equal.
	www.physicsforums.com /showthread.php?p=880109 (1393 words)

	HotDog Express for AOL Hometown Document (Site not responding. Last check: 2007-11-04)
		Determine whether an ordered pair is a solution of an equation
		The order in which the variables appear in an equation does not change the ordered pair.
		We already know that the solution of an equation with two variables is an ordered pair of numbers, which can be plotted on a coordinate plane.
	www.american.edu /edtech/john/kathie3.html (423 words)

	ordered pair
		A collection of two objects such that one can be distinguished as the first element and the other as the second element.
		Ordered triples and ordered n-tuples (ordered lists of n terms) are defined in the same way.
		An ordered triple (a, b, c) can be defined as (a, (b, c)), i.e.
	www.daviddarling.info /encyclopedia/O/ordered_pair.html (147 words)

	nctm
		A location’s street number corresponds to the x-value of an ordered pair if the location is on an east-west street, and the street number corresponds to the y-value of an ordered pair if the location is on a north-south street.
		After the street number is used to find half of an ordered pair, then street maps are used to estimate the other half of the ordered pair.
		The ordered pair which represents Wrigley Field is (-1060, 3600).
	homepage.mac.com /tcanright/plottingpoints/nctm.html (727 words)

	df-op - Metamath Proof Explorer
		There are other ways to define ordered pairs; the basic requirement is that two ordered pairs are equal iff their respective members are equal.
		If we restrict our sets to nonnegative integers, an ordered pair definition that involves only elementary arithmetic is provided by nn0opth 5989.
		Finally, an ordered pair of real numbers can be represented by a complex number as shown by cru 6058.
	us.metamath.org /mpegif/df-op.html (145 words)

	The Cartesian Coordinate System
		Each point in the coordinate plane corresponds to an ordered pair of numbers called its coordinates.
		By thinking of each row in the table as an ordered pair, we can plot the points representing each contestant.
		What we now have is five ordered pairs, which we can place on a graph.
	www.blc.edu /fac/rbuelow/CAL/nt1-3.htm (773 words)

	Greg's Grid Graphs
		An ordered pair is a pair of numbers that name a point on a grid.
		Look at the grid and decide what letter is at each ordered pair.
		Use the ordered pair numbers to locate places on the grid.
	www.beaconlearningcenter.com /WebLessons/GridGraph/default.htm (241 words)

	Films for the Humanities and Sciences - Ordered Pairs
		With the horizontal value first, and the vertical value second, the vector is defined by an ordered pair.
		A ship’s course is used to demonstrate the way in which the ordered pairs of the components of a vector can be added to find the ordered pair of the resultant.
		The resultant of multiple vectors can be found more easily and quickly by adding ordered pairs than by drawing all the vectors and performing calculations.
	www.films.com /id/7048/Ordered_Pairs.htm (339 words)

	3.2 Class Notes
		Note: An equation with two variables has a solution that is an ordered pair.
		Example 1 Determine whether each of the following pairs is a solution of the given equation.
		Plot the ordered pairs and draw a straight line passing through the points.
	mtsu32.mtsu.edu:11197 /3_2_class_notes.htm (202 words)

	ordered pair (Site not responding. Last check: 2007-11-04)
		two ordered numbers; two numbers with a specific first number and a specific second number.
		Ordered pairs are often used to match numbers in relations or functions.
		Ordered pairs which name points are called COORDINATES.
	www.mathnstuff.com /math/spoken/here/1words/o/o9.htm (177 words)

	Beginning Algebra Tutorial on The Rectangular Coordinate System
		Tell if an ordered pair is a solution of an equation in two variables or not.
		Note that you were only given three ordered pairs to check, however, there are an infinite number of solutions to this equation.
		In the ordered pair (1,), is 1 that is given the
	www.wtamu.edu /academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut20_rect.htm (1418 words)

	[No title]
		Pairs because there are 2 and ordered because the order is important.
		The first number in an ordered pair (x, y) is the x-coordinate.
		The second number in an ordered pair (x, y) is the y-coordinate.
	home.att.net /~derfk/unit_15.ppt (923 words)

	Set Operations
		is a pair of objects with an order associated with them.
		For example the ordered pair <1, 2> is not equal to the ordered pair <2, 1>.
		For example the ordered 3-tuple <1, 2, 3> is not equal to the ordered n-tuple <2, 3, 1>.
	www.cs.odu.edu /~toida/nerzic/content/set/set_operations.html (524 words)

	VA-SOL-Lesson Plans
		Students will identify the ordered pair for a point and locate the point for an ordered pair in the first quadrant of a coordinate plane.
		The purpose of this activity is to reinforce a lesson on graphing an ordered pair of numbers by playing a game of battleship.
		Discuss what the students have discovered so far about graphing ordered pairs.
	www.knowledge.state.va.us /cgi-bin/lesview.cgi?idl=487 (271 words)

	Wick's Theorem for the Evaluation of Matrix Elements (Site not responding. Last check: 2007-11-04)
		These reduced terms may be viewed as arising from so-called ``contractions'' between operator pairs.
		That is, the contraction between the operators is simply the original ordering of the pair minus the normal-ordered pair.
		The evaluation of the pairwise contractions may introduce sign changes because the string of operators must be permuted to bring the pair together before the contraction may be evaluated.
	zopyros.ccqc.uga.edu /lec_top/cc/html/node13.html (808 words)

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