Ordered pair definition for math

An ordered pair refers to two numbers written in a certain order. We generally use ordered pairs in the context of coordinates of a point in a 2D plane. It helps to locate or plot a point easily on a Cartesian plane.

An ordered pair, as its name suggests, is a pair of elements that have specific importance for the order of their placements. Ordered pairs are usually used in coordinate geometry to represent a point on a coordinate plane. Also, they are used to represent elements of a relation. An ordered pair is a pair formed by two elements that are separated by a comma and written inside the parantheses. For example, x, y represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair. These elements have specific names according to what context they are being used and they can be either variables or constants. The order of the elements has a certain importance in an ordered pair.

Ordered pair definition for math

In mathematics , an ordered pair a , b is a pair of objects. Ordered pairs are also called 2-tuples , or sequences sometimes, lists in a computer science context of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors. Technically, this is an abuse of terminology 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. For example, the ordered triple a , b , c can be defined as a , b , c , i. In the ordered pair a , b , the object a is called the first entry , and the object b the second entry of the pair. Alternatively, the objects are called the first and second components , the first and second coordinates , or the left and right projections of the ordered pair. Cartesian products and binary relations and hence functions are defined in terms of ordered pairs, cf. The a , b notation may be used for other purposes, most notably as denoting open intervals on the real number line. In such situations, the context will usually make it clear which meaning is intended. 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 notation specifying the two objects a and b , in that order.

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Ordered pair definition for math

An ordered pair consists of two numbers that are written in a fixed order. So, we can define an ordered pair as the pair of elements that occur in a particular order and are enclosed in brackets. An ordered pair is a combination of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses. An ordered pair refers to a number written in a certain order. An ordered pair is used to show the position on a graph, where the "x" horizontal value is first, and the "y" vertical value is second. Also in the co- ordinate system, ordered pair is used to locate a point. Pairs in math are denoted by , and are generally considered to be ordered. To graph a point, we have to draw a dot at the coordinates that correspond to the ordered pair. The x-coordinate tells us how many steps we have to take to on the x-axis.

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Now, we understood the difference between the x-coordinate and y-coordinate of an ordered pair in coordinate geometry. The equality property of ordered pairs says that if two ordered pairs are equal then their corresponding elements are equal. Practice Questions on Ordered Pair. An ordered pair is of the form x, y. Step 3: The point at which we arrive in Step 2 represents the ordered pair x, y. Complete Factor Pairs for a Number Game. This definition works only if the set of natural numbers is infinite. The order of the elements has a certain importance in an ordered pair. Online Tutors. However, as is sometimes pointed out, no harm will come from relying on this description and almost everyone thinks of ordered pairs in this manner. Example 1: Plot the point represented by the ordered pair 6, 4 on the Cartesian plane. Help your child perfect it through real-world application. Here, x is the horizontal distance of the point from the origin and y is the vertical distance of the point from the origin. The signs of x and y in an ordered pair x, y in a particular quadrant can be determined on the basis of the two number lines that form axes of the given quadrant. These elements have specific names according to what context they are being used and they can be either variables or constants.

Welcome to Brighterly , your trusted partner in the journey of learning and understanding mathematics! From the treasure maps of pirate tales to the complex realms of modern mathematics, ordered pairs are pivotal.

Maths Questions. Ordered pairs are also called 2-tuples , or sequences sometimes, lists in a computer science context of length 2. While different objects may have the universal property, they are all naturally isomorphic. Another way to rigorously deal with ordered pairs is to define them formally in the context of set theory. Related Worksheets. The set of all possible ordered pairs from a set A to a set B is called the cartesian product. If two ordered pairs are equal, then their corresponding elements are also equal. The order of the elements has a certain importance in an ordered pair. Bourbaki group in its Theory of Sets , published in The signs of x and y in an ordered pair x, y of a point differs depending upon the quadrant and they are shown in the table below.