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 mistressmercyxox 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 ordered pair definition for math separated by a comma and written inside the parantheses.

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.

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. This is usually followed by a comparison to a set of two elements; pointing out that in a set a and b must be different, but in an ordered pair they may be equal and that while the order of listing the elements of a set doesn't matter, in an ordered pair changing the order of distinct entries changes the ordered pair. This "definition" is unsatisfactory because it is only descriptive and is based on an intuitive understanding of order.

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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. With Brighterly by your side, this journey promises to be illuminating and engaging. An ordered pair is a fundamental concept in mathematics, specifically in set theory and geometry. Consider the ordered pair 3, 5. Importantly, the order of these elements matters.

Ordered pair definition for math

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Since the order of the elements is significant, we cannot interchange the positions of the numbers. Complete Factor Pairs for a Number Game. Then a is in the left hand side, and thus in the right hand side. Correct Incorrect. To represent an ordered pair, the two numbers are written inside the parentheses, separated by a comma, like this:. This definition is acceptable because this extension of ZF is a conservative extension. Use the given ordered pairs to plot the points. A tuple is a finite ordered list of numbers or elements. Commercial Maths. Academic Press. Another way to rigorously deal with ordered pairs is to define them formally in the context of set theory. Example: If 2, 4 is a point on the coordinate plane, then 2 is the distance of the point from the y-axis.

Sets are a collection of well-defined objects.

Cambridge Univ. Let's start from the origin, move to the right by 4 units as 4 is positive and then move down by 3 units as 3 is negative. This is usually followed by a comparison to a set of two elements; pointing out that in a set a and b must be different, but in an ordered pair they may be equal and that while the order of listing the elements of a set doesn't matter, in an ordered pair changing the order of distinct entries changes the ordered pair. Hence if the ordered pair is not taken as primitive, it must be defined as a set. Till now we have seen that ordered pairs are used in coordinate geometry to locate a point. Graphing Ordered Pairs 4. In -2, -3 , both x and y coordinates are negative. An ordered pair gives different meanings depending upon different contexts. A Theory of Sets. Kuratowski : If. 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. This is called "equality property of ordered pairs". In which quadrants do the points — 3, — 5 , 8, 4 , — 7, 5 , 6, — 3 lie on the Cartesian plane? Solution: In 2, -3 , x-coordinate is positive and y-coordinate is negative.