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. Also, they are used to represent elements of a relation.

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.

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.

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Ordered pair definition for math

Their order of appearance is important, so we call them first and second elements respectively. For a complicated problem, divide it into smaller tasks and solve each one separately. Then assemble them to form the final answer. Cartesian products can be extended to more than two sets.

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Online Tutors. Complete Factor Pairs for a Number Game. Our Team. This was the approach taken by the N. For example, 2, -4 refers to 2 on the x-axis positive and -4 on the y-axis negative. The general notion of such definitions or implementations are discussed in Thomas Forster "Reasoning about theoretical entities". Related Games. This "definition" is unsatisfactory because it is only descriptive and is based on an intuitive understanding of order. Select a Pair of Equivalent Fractions Game. Every point on the coordinate plane is represented by an ordered pair x, y where the first element x is called the x-coordinate and the second element y is called the y-coordinate. Why is the order significant in an ordered pair? This renders possible pairs whose projections are proper classes. Ordered Pair in Sets 6. Short: [13]. Set mathematics.

Ordered pairs are sets of numbers used for plotting points.

In type theory and in outgrowths thereof such as the axiomatic set theory NF , the Quine—Rosser pair has the same type as its projections and hence is termed a "type-level" ordered pair. Categories : Basic concepts in set theory Order theory Type theory. Every point on the coordinate plane is represented by an ordered pair x, y where the first element x is called the x-coordinate and the second element y is called the y-coordinate. Commercial Maths. An ordered pair refers to a pair of two numbers or variables written inside brackets and are separated by a comma. Russell's paradox Suslin's problem Burali-Forti paradox. Interpretation function of models Model equivalence finite saturated spectrum submodel Non-standard model of arithmetic Diagram elementary Categorical theory Model complete theory Satisfiability Semantics of logic Strength Theories of truth semantic Tarski's Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity. The set of all possible ordered pairs from a set A to a set B is called the cartesian product. In such situations, the context will usually make it clear which meaning is intended. It is formed by the intersection of two perpendicular number lines or axes. Maths Questions. When you wish to analyze the relationship between two variables where one variable depends on the other, you can use ordered pairs to record data.