Ordered pair definition for math

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.

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.

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. To represent an ordered pair, the two numbers are written inside the parentheses, separated by a comma, like this:. Since the order of the elements is significant, we cannot interchange the positions of the numbers. Thus, x, y may not always be equal to y, x. It is formed by the intersection of two perpendicular number lines or axes. We call the horizontal axis the x-axis and the vertical axis the y-axis. The two axes intersect at the origin. An ordered pair represents the position of a point on the coordinate plane with respect to the origin. The ordered pair 0,0 defines the position of origin.

Let us learn more about ordered pairs along with its definition, meaning, properties, and more.

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Sets are a collection of well-defined objects. In general, we can represent a set in three forms they are statement or description form, roster form, and set builder. The other easy way to represent a set in some situations is an ordered pair. As we already learned that an ordered pair in the coordinate plane has two coordinates namely x-coordinate and y-coordinate. In the same way, ordered pair in the set theory also has two elements. Check the following sections to know more about an ordered pair definition and solved questions.

Ordered pair definition for math

The Cartesian plane is formed by the intersection of two number lines. We use these two number lines to mark points on t his plane. The use of these points is important because they represent specific data points on the plane and indicate relationships in the data represented by the two intersecting number lines. This article will introduce you to the concept of ordered pairs and their importance in coordinate geometry, along with a few sample problems based on this concept.

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For example, 2, -4 refers to 2 on the x-axis positive and -4 on the y-axis negative. A more satisfactory approach is to observe that the characteristic property of ordered pairs given above is all that is required to understand the role of ordered pairs in mathematics. In mathematics , an ordered pair a , b is a pair of objects. Hence this definition has the advantage of enabling a function , defined as a set of ordered pairs, to have a type only 1 higher than the type of its arguments. For example, you can record the number of people visiting a restaurant or a museum in a particular week as 5, 25 , meaning 25 people visited a restaurant on the fifth day Friday. If you change the order, you will get an entirely different location. Each point on the Cartesian plane is represented by an ordered pair x, y. For an extensive discussion of the ordered pair in the context of Quinian set theories, see Holmes Ordered triples which are defined as ordered pairs do not have this property with respect to ordered pairs. Math is a life skill. Our Team. Any subset of the cartesian product is called a relation. Jena: Verlag Hermann Pohle.

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United States. Thus, x, y may not always be equal to y, x. Similarly, you can easily identify in which quadrant a given ordered pair lies. One of the most cited versions of this definition is due to Kuratowski see below and his definition was used in the second edition of Bourbaki's Theory of Sets , published in Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space. An ordered pair gives different meanings depending upon different contexts. Maths Puzzles. Already booked a tutor? Cambridge Univ. Contents move to sidebar hide. Saudi Arabia. This definition works only if the set of natural numbers is infinite. Bourbaki group in its Theory of Sets , published in