Posts Tagged ‘subset’
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
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 22nd, 2009
Inductive Sets in Set Theory
Description
A detailed tutorial on inductive sets in set theory. Step by step tutorial including several examples of inductive sets in set theory for reference.
Overview
An inductive set is a continuous set of natural numbers that follows a basic pattern of n + 1. This means that for all numbers in the set, that number plus the number one must also be included in the set.The set does not need to include all natural numbers – that is, the set may start at any natural number provided it is greater than or equal to one. However, the set must continue to infinity or it cannot be considered an inductive set.
Tags: -1, addition, complete, continuous, discrete math, element, equal, greater, induction, inductive, infinity, mathematical, natural, numbers, one, pattern, principle, set, subset, theory
Posted in Discrete Math | No Comments »
Tuesday, October 20th, 2009
Families of Sets in Set Theory
Description
A detailed tutorial on families of sets. Step by step tutorial including several examples of families or collections of sets for reference.
Overview
Families of sets are closely linked with indexed sets – the only sets that can be indexed are families of sets. A family of sets is basically a set of sets. An example would be a power set (the set of all subsets of a set). Unions and intersections can also be performed with families of sets. Instead of concerning just two sets, they concern every single set in the family of sets. The union and intersection over a family of sets are known as extended set operations.
Tags: collections, discrete math, elements, extended, families, index, indexed, intersection, operations, power set, set, set theory, subset, union
Posted in Discrete Math | No Comments »
Thursday, October 15th, 2009
Complements in Set Theory
Description
A detailed tutorial on complements in set theory. Step by step tutorial including several examples of complements in set theory for reference.
Overview
In set theory, a complement is the opposite of something. It works a little like negation, in that the complement of a set is everything but that set. The way to find this is to subtract the set from its universe, which is a larger set that the set you are taking a complement of belongs to. You can think of your set as a subset of the universe.
Tags: complement, discrete math, elements, Math, negation, opposite, set, set theory, subset, universe
Posted in Discrete Math | No Comments »
Thursday, October 15th, 2009
Difference in Set Theory
Description
A detailed tutorial of difference in set theory. Step by step tutorial including several examples of difference in set theory for reference.
Overview
Difference is what you get after subtracting two numbers – or two sets. As with other examples of subtraction, order is very important for difference in set theory. Unless two sets are identical, you will end up with a different answer depending on the order. Difference is very often used in conjunction with union and intersection of sets or power sets.
Tags: difference, discrete math, element, empty set, intersection, Math, number, order, power set, set, set theory, subset, subtract, subtraction, union
Posted in Discrete Math | No Comments »
Tuesday, October 13th, 2009
Empty Set in Set Theory
Description
A detailed tutorial on the empty set. Step by step tutorial including several examples and a description of the properties of the empty set for reference.
Overview
The empty set is a unique set in set theory that means a set composed of nothing. In an empty set, there are no elements at all. The empty set has one very unique property – it is the subset of all sets. The set of all natural numbers up to infinity? It’s a subset. The set of prime numbers less than 20? It’s a subset of that, too. It is also a subset of itself – although that is not particurarly unique. The empty set is not used in equations, but can be used to define them.
Tags: difference, discrete math, element, empty set, intersection, Math, none, set, set theory, subset, union, unique, zero
Posted in Discrete Math | No Comments »
Tuesday, October 13th, 2009
Power Sets in Set Theory
Description
A detailed tutorial on power sets. Step by step tutorial including several examples of power sets and how to perform operations of power sets for reference.
Overview
Power sets are defined as a set of all subsets. So for example, say you have a set A. The power set of A would be the set of all possible subsets of A. Power sets can also be used in normal operations, such as intersections and unions. All you do is find all possible subsets of both sets you are working with, and solve the problem like you would with a normal set.
Tags: difference, discrete math, element, empty set, intersection, Math, power, set, set theory, subset, union
Posted in Discrete Math | No Comments »
Thursday, October 8th, 2009
Subsets in Set Theory
Description
A detailed tutorial on how to identify subsets of a set. Step by step tutorial including several examples of how to find subsets in a set for reference.
Overview
Each set in set theory has a certain amount of subsets. There is an easy way figure out how many subsets a set has. Pretend that every element of a set is 2, and multiply them together. This will be your number of subsets. For example, if you have three elements, you will have 8 subsets, because 2 cubed (which is 2 to the power of 3, or 2 times 2 times 2) is equal to 8. Now that you have determined how many subsets there are, you have to figure out what they are. A subset is defined as any set containing all or part of a set. Two subsets are going to be the set itself, and an empty set. Sometimes they are your only subsets. Now, following the definition, a subset must be all possible sets. This means, sets of one element - one for each element in your set. In addition to that, you may have sets of two elements – one for each possible combination of elements in your set. This should be continued until you have reached the maximum number of elements in the set you atarted out with.
Tags: combination, discrete math, element, empty set, exponent, Math, multiplication, number, set, set theory, subset, to the power, value
Posted in Discrete Math | No Comments »
