Summary
- A pair of numbers written in a particular order and enclosed in brackets are known as ordered pairs.
- And ordered pair is represented as, Ordered Pair = (x, y)
- The ordered pair changes based on the change in the position of the elements of the ordered pair.
How do you calculate ordered pairs?
Ordered Pair explanation. Ordered Pair = (x, y) where, x = abscissa, the distance measure of a point from the x-axis. and, y = ordinate, the distance measure of a point from the y-axis. To graph a point, we have to draw a dot at the coordinates that correspond to the ordered pair.
What are the numbers in an ordered pair called?
Summary
- A pair of numbers written in a particular order and enclosed in brackets are known as ordered pairs.
- And ordered pair is represented as, Ordered Pair = (x, y)
- The ordered pair changes based on the change in the position of the elements of the ordered pair.
Which ordered pairs are solutions of each equation?
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4,7) ( 4, 7) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.
What is the first number in an orderd pair called?
Ans: The first number in the ordered pair is called the x coordinate or abscissa. The second number in the ordered pair called the y coordinate or ordinate. Q2. Why do we Use Ordered Pairs? Ans: Ordered pairs help to locate a point on the Cartesian plane for better visual comprehension.
How do you know if an ordered pair is a function?
A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.
What is a function in ordered pairs example?
To represent a function using ordered pairs, we use ordered pairs in which the first coordinates are the inputs and the second coordinates are the corresponding outputs. For example, in our calorie example, we have that the broccoli has 50 calories, so broccoli is our input, and 50 is our output.
What makes an ordered pair not a function?
In order for a relation to be a function, each x must correspond with only one y value. If an x value has more than one y-value associate with it -- for example, in the relation {(4, 1), (4,2)}, the x-value of 4 has a y-value of 1 and 2, so this set of ordered pairs is not a function.
How can you identify if the set of ordered pairs is not function?
How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!
How can you identify a function?
You can use the vertical line test on a graph to determine whether a relation is a function. If it is impossible to draw a vertical line that intersects the graph more than once, then each x-value is paired with exactly one y-value. So, the relation is a function.
How do you determine a function?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
How do you write an ordered pair?
As per the definition of ordered pair, the point P will be written as:P = (6, 4)The first number in the ordered pair shows the distance from “x” axis which is 6.The second number in the ordered pair shows the distance from “y” axis which is 4.
How do you know if the graph is a function?
key idea. You can use the vertical line test on a graph to determine whether a relation is a function. If it is impossible to draw a vertical line that intersects the graph more than once, then each x-value is paired with exactly one y-value. So, the relation is a function.
What is any set of ordered pairs called?
A relation is any set of ordered pairs. The set of all first components of the ordered pairs is called the domain. The set of all second components is called the range.
What is relation and function example?
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function. For example: Domain. Range. -1.
What is a function and not a function?
A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.
Which of the following is an example of an ordered pair?
An ordered pair is a pair of numbers in a specific order. For example, (1, 2) and (- 4, 12) are ordered pairs. The order of the two numbers is important: (1, 2) is not equivalent to (2, 1) -- (1, 2)≠(2, 1).
How do you tell if a table is a function?
How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!
Why is the order pair important in geometry?
The concept of ordered pair is highly useful in data comprehension as well for word problems and statistics. The coordinate geometry uses ordered pairs to represent geometric figures and objects in an open space for visual comprehension.
Which geometric shapes use ordered pairs?
Geometric shapes like circle, triangle, square, rectangle and polygons use the ordered pairs to represent the center, vertices and the length of the sides with coordinates. Fun facts. The mathematician Rene Descartes and Pierre de Fermat invented analytic geometry in 16th century and Cartesian plane was designed.
Why is it important to locate a point on the Cartesian plane?
It helps to locate a point on the Cartesian plane for better visual comprehension.
What is the point where two lines meet in the Cartesian plane?
In the Cartesian plane, we define a two-dimensional space with two perpendicular reference lines, namely x-axis and y-axis. The point where the two lines meet at “0” is the origin.
How to mark a point on a Cartesian plane?
To mark the point on the Cartesian plane, start from the origin. Take 6 steps towards the “x” axis (towards right) starting from the origin. From here, take 4 steps towards the “y” axis (upwards). As the name “ordered pair” suggests, the order in which values are written in a pair is very important.
Can Ordered Pairs Be A Function?
A set of ordered pairs can be a function, but only in a special case (more on this below).
Can An Ordered Pair Have Three Numbers?
An ordered pair cannot have three numbers. An ordered pair is defined to be two numbers (or items).
Can An Ordered Pair Have A Fraction?
An ordered pair can have a fraction, decimal, or radical as one of the items. For example, the following are all valid ordered pairs:
How To Graph An Ordered Pair
To graph an ordered pair (a, b), you can think of it as finding the intersection between two lines:
How To Graph A Relation
To graph a relation, we simply graph the entire set of all ordered pairs in the relation.
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What is an ordered pair?
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 .)
What is the first entry of an ordered pair?
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.
What is Quine's theory of order pair?
^ Quine has argued that the set-theoretical implementations of the concept of the ordered pair is a paradigm for the clarification of philosophical ideas (see " Word and Object ", section 53). The general notion of such definitions or implementations are discussed in Thomas Forster "Reasoning about theoretical entities".
What is the product of a category?
A category-theoretic product A × B in a category of sets represents the set of ordered pairs, with the first element coming from A and the second coming from B. In this context the characteristic property above is a consequence of the universal property of the product and the fact that elements of a set X can be identified with morphisms from 1 (a one element set) to X. While different objects may have the universal property, they are all naturally isomorphic .
What are the disadvantages of a short pair?
Yet another disadvantage of the short pair is the fact, that even if a and b are of the same type, the elements of the short pair are not. (However, if a = b then the short version keeps having cardinality 2, which is something one might expect of any "pair", including any "ordered pair".
What is the set of all ordered pairs whose first entry is in some set A and whose second entry is in?
The set of all ordered pairs whose first entry is in some set A and whose second entry is in some set B is called the Cartesian product of A and B , and written A × B. A binary relation between sets A and B is a subset of A × B .
When did Kuratowski define ordered pairs?
In 1921 Kazimierz Kuratowski offered the now-accepted definition of the ordered pair ( a, b ):
How to use ordered pairs in math?
To represent a function using ordered pairs, we use ordered pairs in which the first coordinates are the inputs and the second coordinates are the corresponding outputs. For example, in our calorie example, we have that the broccoli has 50 calories, so broccoli is our input, and 50 is our output. To use an ordered pair to show this, we have broccoli as our first coordinate and 50 as our second coordinate. That is, (broccoli, 50). To represent our whole function using ordered pairs, we list each of the ordered pairs within brackets.
What is an ordered pair table?
An ordered pair consists of two elements separated by a comma and enclosed in parentheses.
What is the relationship between two sets of inputs and outputs called?
The relationship that relates the type of food to its caloric content is called a function. In mathematics, a function is a relationship between two sets, called inputs and outputs, where each input is related to exactly one output. Because of this, in a function, we can determine an output given an input.
How to describe a function?
A function is a relationship between two sets of elements, called the inputs and the outputs, in which each input has exactly one output. There are many representations of functions. One way to represent a function is by using ordered pairs, where an ordered pair consists of two elements separated by a comma and enclosed by parentheses. We call the first element of an ordered pair the first coordinate, and we call the second element of an ordered pair the second coordinate.
Why is it important to have multiple ways to represent a function?
Different functions call for different representations, so having multiple ways to represent a function is quite useful when working with functions Thus, it is good that we are now familiar with one more way of representing these mathematical concepts.
Is ordering pairs a good representation?
That's not too hard, it is? As we said, there are a number of ways to represent a function, and using ordered pairs is just one of them. This is a good representation to use when there are a finite number of inputs and outputs making up the function, just like in our calorie example. If there are an infinite number of inputs and outputs, then it would be impossible to list them all. This is why this representation is best used in the case of a finite number of inputs and outputs.
Why is the first set of ordered pairs not a function?
The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. The second example is not a function, because it contains the ordered pairs (1,2) and (1,5). These have the same first coordinate and different second coordinates.
How to represent a function?
A function can be represented using ordered pairs. We simply write the inputs as the first coordinates and the outputs as the second coordinates. Consider our dessert menu example. We would represent this using ordered pairs like this:
How to tell if a graph is a function?
Notice that if there are two points with the same first coordinate and different second coordinates, we can draw a vertical line through them. Since a graph that is a function can't contain two points like this, it makes sense that a vertical line drawn anywhere on the graph should only intersect the graph once. This is called the vertical line test, and it states that a graph is a function if a vertical line drawn anywhere on that graph only intersects the graph once.
How to use tables to represent functions?
We can use tables to represent functions by listing the input values in one column and the corresponding output values in another column. Let's look at our dessert function using a table.
What is a function in math?
A function is a relationship in which one variable is determined by the other variable. In a function, each input has exactly one output, so if a relationship has an input that has more than one output, that relationship is not a function. We can represent functions in many different ways. For instance, we can use words, mappings, ordered pairs, ...
What is relationship in math?
In general, a relationship is a function if for every input, there is exactly one output. When this is the case, we can determine the output based on the input. Let's consider a few more representations of functions and how to identify a function from these representations.
Can a set of ordered pairs have more than one output?
By our function rule, no input can have more than one output, so a set of ordered pairs is a function as long as no two ordered pairs have the same first coordinate with different second coordinates. This is illustrated here:
Ordered Pair Explanation
- Ordered Pair = (x, y) where, x = abscissa, the distance measure of a point from the x-axis. and, y = ordinate, the distance measure of a point from the y-axis. 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 step…
Example of An Ordered Pair
- The ordered pair (2, 5) means a pair of two integers, strictly in the order with 2 at the first place called the abscissa and 5 at the second place called the ordinate. The ordered pair (2, 5) is not equal to the ordered pair (5, 2) because (2, 5) ≠ (5, 2). Therefore, in a pair, the order of elements is important.
Set of Ordered Pairs
- The pair of elements that occur in a particular order and are enclosed in brackets is known as a set of ordered pairs. If ‘a’ and ‘b’ are two elements, then the two different pairs are (a, b), (b, a). In an ordered pair (a, b), a is called the first element, and b is called the second element. Consider, if A and B are two sets such that a ∈ A and b ∈ B, then by the ordered pair of elements we mean (a…
Properties of Ordered Pairs
- Equality of Ordered Pairs Two ordered pairs are said to be equal if and only if the corresponding first elements are equal and the corresponding second elements are equal. For example: Consider two ordered pairs (a, b) and (c, d). They are equal if a = c and b = d, i.e., (a, b) = (c, d). Question: Find the values of x and y, if (2x - 3, y + 1) = (x + 5, 7) Solution: We will solve by equality of ordere…
Solved Examples
- 1. Plot the point “P” with coordinates 6, 4. Sol:As per the definition of ordered pair, the point P will be written as: P = (6, 4) The first number in the ordered pair shows the distance from the “x" axis which is 6. The second number in the ordered pair shows the distance from the “y" axis which is 4. To locate the point on the Cartesian plane, start from the origin. Take 6 steps towards the “x” axi…
Fun Facts
- The mathematician Rene Descartes and Pierre de Fermat invented analytic geometryin the 16th century and the Cartesian plane was designed.
- Ordered pair is widely used in the field of computing and programming languages.
- Ordered pairs are also known as 2-tuples, or sequences of length 2.
Summary
- A pair of numbers written in a particular order and enclosed in brackets are known as ordered pairs.
- And ordered pair is represented as, Ordered Pair = (x, y)
- The ordered pair changes based on the change in the position of the elements of the ordered pair.
- A pair of numbers written in a particular order and enclosed in brackets are known as ordered pairs.
- And ordered pair is represented as, Ordered Pair = (x, y)
- The ordered pair changes based on the change in the position of the elements of the ordered pair.
- It is used in statistics, to depict the center and vertices of a circle, square, rectangle, and others.
Can Ordered Pairs Be A function?
- A set of ordered pairs can be a function, but only in a special case (more on this below). First, an ordered pair is a single pair of items, such as (1, 3). A relation is a set of one or more ordered pairs. For example, the set {(1, 3)} is a relation (this relation only has one ordered pair). The set {(1, 3), (2, 5)} is also a relation (this relati...
Can An Ordered Pair Have Three numbers?
- An ordered pair cannot have three numbers. An ordered pair is defined to be two numbers (or items). However, an ordered triple does have three numbers. An ordered triple is a set of three items (a, b, c) where the order of the items matters. The only way that two ordered triples (a, b, c) and (d, e, f) are the same is if a = d, b = e, and c = f. For example, all of the following ordered tripl…
Can An Ordered Pair Have A fraction?
- An ordered pair can have a fraction, decimal, or radical as one of the items. For example, the following are all valid ordered pairs: 1. (1/5, 6) 2. (5.7, 2/3) 3. (7/2, 6/5) 4. (√7, 3) The exception is if we restrict the items to a particular set of numbers. For example, if we restrict the items in an ordered pair to rational numbers, then there can be no radicals. In that case, (√7, 3) would not b…
How to Graph An Ordered Pair
- To graph an ordered pair (a, b), you can think of it as finding the intersection between two lines: 1. The vertical line x = a 2. The horizontal line y = b Since a vertical line and a horizontal line are perpendicular, they will intersect at exactly one point: (a, b), which corresponds to this ordered pair on a graph in 2-dimensional space (a coordinate plane).
Overview
In mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.)
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. (Tech…
Defining the ordered pair using set theory
If one agrees that set theory is an appealing foundation of mathematics, then all mathematical objects must be defined as sets of some sort. Hence if the ordered pair is not taken as primitive, it must be defined as a set. Several set-theoretic definitions of the ordered pair are given below( see also ).
Norbert Wiener proposed the first set theoretical definition of the ordered pair in 1914:
Generalities
Let and be ordered pairs. Then the characteristic (or defining) property of the ordered pair is:
The set of all ordered pairs whose first entry is in some set A and whose second entry is in some set B is called the Cartesian product of A and B, and written A × B. A binary relation between sets A and B is a subset of A × B.
The (a, b) notation may be used for other purposes, most notably as denoting open intervals on the real …
Informal and formal definitions
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 an…
Category theory
A category-theoretic product A × B in a category of sets represents the set of ordered pairs, with the first element coming from A and the second coming from B. In this context the characteristic property above is a consequence of the universal property of the product and the fact that elements of a set X can be identified with morphisms from 1 (a one element set) to X. While different obje…