Posts Tagged ‘ordered pair’
Tuesday, October 27th, 2009
The Range of Relations
Description
A detailed tutorial on the range of relations. Step by step tutorial including several examples of the range of relations for reference.
Overview
The range of a relation is denoted as Rng(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The range is the set of all the y endpoints – that is to say, all the endpoints that come second in the ordered pair. If you are taking the range of the inverse of a relation, then that would be all the x endpoints. When writing the range, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, element, endpoint, ordered pair, range, relations, second, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Domain of Relations
Description
A detailed tutorial on the domain of relations. Step by step tutorial including several examples of the domain of relations for reference.
Overview
The domain of a relation is denoted as Dom(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The domain is the set of all x endpoints – that is to say, all the endpoints that come first in the ordered pair. If you are taking the domain of the inverse of a relation, then that would be all the y endpoints. When writing the domain, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, domain, element, endpoint, First, ordered pair, relations, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
The Inverse of Relations
Description
A detailed tutorial on the inverse of relations. Step by step tutorial including several examples of the inverse of relations for reference.
Overview
Inverse is a term you should be familiar with. An inverse operation is one that undoes the original operation. But what is an inverse relation? When you take the inverse of a relation, you are switching the endpoints in every ordered pair in the original relation. For each ordered pair in the relation, instead of being written as (x, y) it will now be written as (y, x).
Tags: cartesian, coordinates, discrete math, endpoint, inverse, operation, ordered pair, relations, x, y
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
An Introduction to Relations
Description
A detailed tutorial on the introduction to relations. Step by step tutorial including several examples of the introduction to relations for reference.
Overview
A relation is defined as an ordered pair. However, that is not entirely accurate. A relation could either be an ordered pair or a set of ordered pairs. A relation can be used with either one or more normal sets, or one Cartesian product set. When used with a normal set, it is a set of ordered pairs. When used with a Cartesian product, it is the power set of that set.
Tags: cartesian, coordinates, discrete math, element, ordered pair, power, product, relation, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 27th, 2009
Cartesian Products in Set Theory
Description
A detailed tutorial of Cartesian products in set theory. Step by step tutorial including several examples of Cartesian products in set theory for reference.
Overview
A Cartesian product is an operation that can be performed in set theory. It is named not for the multiplication that occurs, but for the way the resulting set is written: it is written in ordered pairs, just like Cartesian coordinates. Two sets are said to be multiplied, such as A and B. Whichever set is written first in the operation has its first coordinate written with the second coordinate of the second set. This continues until all coordinates have been used at least once.
Tags: cartesian, coordinates, discrete math, element, multiplication, operation, ordered pair, product, set, subset, theory
Posted in Discrete Math | No Comments »
Thursday, October 15th, 2009
Definition of Open and Closed Intervals
Description
A detailed tutorial on open and closed intervals. Step by step tutorial including several examples of open and closed intervals for reference.
Overview
An interval is a set of real numbers, expressed by an ordered pair. There are two types of intervals, open intervals and closed intervals. An open interval is an interval written with parenthesis. It implies that the endpoint is not included in the set. A closed interval is an interval written with brackets. It implies that the endpoint is included in the set. It is possible for one endpoint of an interval to be closed, and for the other to be open.
Tags: algebra, bounded, brackets, closed, coordinates, element, endpoint, interval, Math, open, ordered pair, parenthesis, real numbers, set
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Ordered Pairs Explained
Description
A detailed tutorial on ordered pairs. Step by step tutorial including several examples of how to solve problems using ordered pairs for reference.
Overview
An ordered pair is a set of two elements that is in a specific order, that is, (a, b) would be different from (b, a), unless a = b. In ordered pairs, the order of the elements are extremely important. And example of a well-known ordered pair would be a Cartesian coordinate.
Tags: a, arithmetic, b, cartesian, coordinate, element, equals, graph, Math, order, ordered pair, pair, set
Posted in Arithmetic | No Comments »
